f 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 


GIFT  OF 

Henry  Strickland 


ELEMENTARY 
MAGNETISM  AND  ELECTRICITY 


UNIVERSITY  OF  WISCONSIN 
EXTENSION  TEXTS 


A  series  of  Industrial  and  Engineering  Education  Textbooks, 

developed  under  the"direction  of  Dean  Louis  E.  REBER, 

University  of  Wisconsin  Extension  Division 


Norris  and  Smith's 
SHOP  ARITHMETIC 

Norris  and  Craigo's 

ADVANCED     SHOP     MATHEMA- 
TICS 

Hills' 

MACHINE  DRAWING 

George's 

ADVANCED  SHOP  DRAWING 

Wooley  and  Meredith's 
SHOP  SKETCHING 

l.ongfield's 

SHEET  METAL  DRAFTING 

Hobbs,  Elliott  and  Consoliver's 
GASOLINE  AUTOMOBILE 

Norris,  Winning  and  Weaver's 
GAS  ENGINE  IGNITION 

Consoliver  and  Mitchell's 

AUTOMOTIVE       IGNITION 
SYSTEMS 

Shealy's 
HEAT 

Shealy's 

STEAM  BOILERS 

Shealy's 

STEAM  ENGINES 


Jansky's 

THEORY    AND    OPERATION    OF 
D.  C.  MACHINERY 

Jansky's 
ELECTRIC  METERS 

Jansky's 

ELEMENTARY  MAGNETISM  AND 
ELECTRICITY 

Jansky's 

PRINCIPLES      OF      RADIOTELE- 
GRAPHY 

Jansky  and  Faber's 

PRINCIPLES      OF      THE      TELE- 
PHONE 
Part     I. — Subscribers'     Apparatus 

Hool's 

ELEMENTS  OF  STRUCTURES 

Hool's 

REINFORCED    CONCRETE    CON- 
STRUCTION 

Vol.  I. — Fundamental        Principles 
Vol.  II.— Retaining       Walls       and 

Buildings 
Vol.  III. — Bridges  and  Culverts 

Blair's 

SHOW-CART?  WRITING 

Puher's 

MATERIALS  OF  CONSTRUCTION 


£ 

fcs£ 


"§ 

•8 

I 
1 


INDUSTRIAL   EDUCATION   SERIES 

ELEMENTAEY 
MAGNETISM  AND  ELECTRICITY 


PREPARED  IN  THE 

EXTENSION  DIVISION  OF 
THE  UNIVERSITY  OF  WISCONSIN 


BY 
CYRIL  M.  JANSKY,  B.  S.,  B.  A. 

ASSOCIATE    PROFESSOR   OP   ELECTRICAL   ENGINEERING 
THE    UNIVERSITY   OP  WISCONSIN 


FIRST  EDITION 
FIFTH  IMPRESSION 


McGRAW-HILL  BOOK  COMPANY,  INC. 
NEW  YORK:  370  SEVENTH  AVENUE 

LONDON:  6  &  8  BOUVERIE  ST.,  E,  C.  4 

1914 


COPYRIGHT,  1914,  BY  THE 
MCGRAW-HILL  BOOIL  COMPANY,  INC. 


PRINTED   IN   THE   UNITED   STATES   OF   AMERICA 


ACCESS.  HO. 


GIFT 


THE  MAPLE  PRESS  -  YORK  PA 


G?C5(9 


PREFACE 

In  the  preparation  of  this  text,  the  author  has  had  in  mind 
the  needs  of  students  who  may  have  had  some  practical  ex- 
perience with  electrical  apparatus  or  machinery,  but  whose 
knowledge  of  the  principles  of  its  operation  and  of  mathematics 
is  limited.  To  make  magnetic  and  electric  principles  real  to 
such  students,  the  subject  is  developed  experimentally.  The 
student  is  expected  to  perform  simple  experiments  and  thus  to 
observe  the  actual  phenomena.  Then  by  questions  and  dis- 
cussions he  is  aided  in  the  interpretation  of  his  observations, 
and  the  formulation  of  his  conclusions  into  workable  ideas. 

In  order  that  the  subject  may  interest  men  in  the  electrical 
industries  who  are  not  technically  trained,  some  practical  ap- 
plications of  the  fundamental  magnetic  and  electric  principles 
are  illustrated  and  described.  It  is  the  writer's  experience  that 
such  a  presentation  appeals  strongly  to  the  industrial  worker 
who  wishes  to  understand  the  how  and  why  of  things  electrical. 

The  text  is  intended  for  individual  or  home  study,  although 
it  may  be  used  in  class  work  when  a  supply  of  apparatus  is 
available.  This  apparatus  is  inexpensive  and  most  of  it  can 
be  made  by  ^an  ingenious  student.  It  need  not  be  exactly  like 
that  described  in  the  text.  The  conversational  style  in  which 
the  work  is  written  has  been  found  very  helpful  in  correspondence 
instruction  as  it  seems  to  establish  a  personal  relation  between 
the  student  and  instructor. 

Although  the  text  has  been  prepared  for  use  in  correspondence 
instruction,  it  is  hoped  that  it  may  be  of  service  to  continuation 
schools,  Y.  M.  C.  A.  schools,  and  plant  schools  that  give  a  course 
of  like  nature. 

The  author  is  under  obligation  to  Mr.  G.  G.  Thompson, 
engineer  of  the  Cutler  Hammer  Company,  for  reading  the  manu- 
script and  for  making  many  valuable  suggestions,  and  to  Mr. 
G.  R.  Wells  for  making  the  line  drawings.  The  author  also 
wishes  to  express  his  appreciation  of  the  kindness  of  the  various 
manufacturers  of  electrical  apparatus  and  machinery  who  have 
furnished  illustrative  material. 

C.  M.  J. 

THE  UNIVERSITY  OF  WISCONSIN, 
MADISON,  WISCONSIN, 
January,  1914. 

vii 


CONTENTS 

PAGE 
PREFACE vii 

CHAPTER  I 

MAGNETISM 1 

Introduction — Magnetism — Magnets — Permanent  and  Temporary 
Magnets — Forms  of  Magnets — Experiment  1,  Poles  of  a  Magnet — 
Experiment  2,  Laws  of  Magnetic  Attraction — Experiment  3,  Varia- 
tion of  Attraction  with  Distance — Theory — Unit  Pole — Properties 
of  the  Space  Surrounding  a  Magnet — Experiment  4,  Magnetic  Field 
— Theory — Unit  Magnetic  Field — Representation  of  a  Magnetic 
Field — Experiment  5,  Magnetic  Field  Around  Two  Bar  Magnets — 
Theory — Magnetism  a  Molecular  Property — Experiment  6, 
Molecular  Theory  of  Magnetism — Theory — Magnetic  Induction — 
Experiment  7,  Magnetic  Induction — Theory — Experiment  8, 
Effect  of  Heat  on  Magnetism — Theory — Magnetism  of  the  Earth 
— Experiment  9,  Terrestrial  Magnetism — Theory — Declination — 
Dip — Practical  Uses  of  Permanent  Magnets — Recapitulation. 

CHAPTER  II 

ELECTROMAGNETISM 23 

Introduction — Experiment  10,  Magnetic  Field  Around  an  Electric 
Wire — Experiment  11,  Effect  of  an  Electric  Current  Upon  a  Mag- 
netic Needle — Experiment  12,  Properties  of  Solenoids — Theory — 
Rule  for  the  Direction  of  Magnetic  Lines — Rule  for  the  Direction 
of  Current  Flow — Strength  of  Magnetic  Field  Around  an  Electric 
Wire — Reaction  between  Electric  Wires — Magnetic  Field  at  the 
Center  of  a  Circular  Coil — Definition  of  Unit  Current — Electromag- 
nets— Experiment  13,  Development  of  Magnetism  in  an  Iron  ore  by 
an  Electric  Current — Experiment  14,  Magnetic  Properties  of  a 
U-shaped  Bar — Theory — Magnetic  Field  Inside  of  a  Long  Solenoid 
— Permeability — Curve  Plotting — Signs  of  the  Coordinates — 
Plotting — Magnetomotive  Force — Magnetic  Hysteresis — Recapi- 
tulation. 

CHAPTER  III 

SOME  PRACTICAL  APPLICATIONS  OF  ELECTROMAGNETS 47 

Experiment  15,  The  Construction  and  Operation  of  the  Electric 
Bell— The  Telegraph— Experiment  16,  The  principles  of  the  Tele- 
graph— Theory — The  Telephone — Experiment  17,  The  Principles 
of  the  Telephone  Receiver — Theory — Lifting  Magnets — Lifting 
Force  of  Electromagnets — Traction  and  Magnetizing  Force — Re- 
capitulation. 

ix 


x  CONTENTS 

PAGE 

CHAPTER  IV 

ELECTROMAGNETIC  INDUCTION 65 

Introduction — Experiment  18,  To  Study  Electromagnetic  Induc- 
tion— Theory — Law  of  Electromagnetic  Induction — Unit  of  In- 
duced E.  M.  F. — Experiment  19,  Induction  of  an  E.  M.  F.  by  Elec- 
tromagnets— The  Development  of  anE.  M.  F.  by  Electromagnets 
— Theory — Relation  between  Primary  Current  and  Induced 
E.  M.  F. — Practical  Applications — Self  Induction — Experiment 
20,  To  Study  the  Cause  of  Sparking  at  the  Break  in  the  Circuit  of 
Electric  Bell — Theory — Analogies — Self  Inductance — Practical 
Applications — Recapitulation. 

CHAPTER  V 

CURRENT  ELECTRICITY 89 

Introduction — Experiment  21,  The  Simple  Voltaic  Cell — Theory — 
Definitions — Volt-ammeter — Experiment  22,  Electromotive  Force 
or  Pressure — Theory — Volt — Expenditure  of  Energy  in  a  Circuit- 
Experiment  23,  To  Study  Polarization — Theory — Kinds  of  Cells — 
One-fluid  Cells— Edison  Cell— Two-fluid  Cells— Gravity  Cells— Ex- 
periment 24,  Electromotive  Force  of  Different  Cells — Theory — 
Practical  Applications  of  Cells — Recapitulation. 

CHAPTER  VI 

ELECTROLYSIS 105 

Introduction — Liquid  Conductors — Experiment  25,  Electrolytic 
Decomposition — Theory — Anode  and  Cathode — Dissociation  The- 
ory— Faraday's  Law — Electric  Current — Definitions — Coulomb 
— Electrochemical  Equivalent — Secondary  or  Storage  Cells — Ex- 
periment 26,  Principles  of  the  Storage  Battery — Theory — The 
*  Lead  Storage  Cell — The  Nickel-Iron  Storage  Cell — Electroplating 
— Voltages  for  Electroplating — Critical  Current  Density — Electro- 
typing — Gold  and  Silver  Plating — Refining  of  Metals — Some 
Other  Electrolytic  Processes — Recapitulation. 

CHAPTER  VII 

RESISTANCE 123 

Introduction — Electrical  Resistance — Experiment  27,  To  Deter- 
mine the  Relation  Between  Current  and  Length  of  Conductor 
When  Pressure  is  Kept  Constant — Theory — Experiment  28,  To 
Study  the  Relation  between  Size  of  Wire  and  Current — Theory — 
Wire  Measurement — The  Mil — Circular  Mil — Gage  Numbers — 
Theory — Effect  of  Material  Upon  the  Resistance  of  a  Wire — 
Experiment  29,  To  Study  the  Dependence  of  the  Resistance  of  a 
Conductor  on  the  Material  of  Which  It  is  Made — Theory — Unit 
of  Resistance — Calculation  of  Resistance — Resistivity  or  Specific 


CONTENTS  xi 

PAGE 

Resistance — Change  of  Resistance  with  Temperature — Experi- 
ment 30,  To  Study  the  Effect  of  Temperature  upon  Resistance — 
Theory — Practical  Applications — Temperature  Coefficient  of  Re- 
sistance— Resistance  of  Contacts — Recapitulation. 

CHAPTER  VIII 

FLOW  OF  CURRENT  IN  A  CIRCUIT 143 

Introduction — Ohm's  Law — Experiment  31,  To  Verify  Ohm's  Law 
— Theory — Capacity — Resistances  in  Series — Experiment  32,  To 
Study  Resistances  in  Series — Voltage  Drop — Experiment  33,  To 
Show  that  Voltage  Drop  Equals  Product  of  Current  by  Resistance 
— Theory — Resistances  in  Parallel — Experiment  34,  To  Study 
Resistances  of  Conductors  in  Parallel — Theory — Calculation  of 
Joint  Resistance — Three  or  More  Conductors  in  Parallel — Prac- 
tical Applications — Cells  in  Series — Experiment  35,  To  Study  the 
Pressure  of  Cells  in  Series — Theory — Battery  Resistance  for  Series 
Connection — Cells  in  Parallel — Battery  Resistance  of  Parallel 
Connections — Series  Parallel  Connection — Ohm's  Law  Applied  to 
Cells  in  Series  and  Parallel — Best  Grouping  of  Cells — Recapitula- 
tion. 

CHAPTER  IX 

ELECTRIC  GENERATOR  AND  MOTOR 171 

Introduction — The  Generator — Experiment  36,  To  Study  Prin- 
ciples of  the  Electric  Generator — Theory — Experiment  37,  To 
Study  the  Relation  of  Induced  Electromotive  Force  to  Speed — 
Theory — Experiment  38,  To  Study  the  Relation  between  the 
Strength  of  Magnetic  Field  and  Induced  Electromotive  Force — 
Theory — Kinds  of  Generators — Series  Generator — Shunt  Generator 
— Compound  Generator — The  Electric  Motor — Experiment  39, 
To  Investigate  the  Cause  of  Rotation  of  Motor  Armature — 
Theory — Experiment  40,  To  Determine  the  Direction  of  Rota- 
tion— Experiment  41,  To  Investigate  the  Relation  between  the 
Strength  of  Magnetic  Field  and  the  Speed  of  Rotation — Theory 
— Experiment  42,  To  Study  the  Characteristics  of  a  Separately 
Excited  Motor — Theory — Experiment  43,  To  Study  the  Opera- 
tion of  a  Series  Motor — Theory — Experiment  44,  To  Study  the 
Shunt  Motor — The  Compound  Motor — Recapitulation. 

CHAPTER  X 

WORK  AND  ENERGY 193 

Work — Uuit  of  Work — Energy — Power — Units  of  Power — Elec- 
tricity— Electrical  Work — Power  Drop — Heating  Value  of  the 
Electrical  Current — Some  Practical  Applications  of  the  Heating 
of  Electric  Currents — Cost  of  Electric  Heating — Recapitulation. 

INDEX    ,  ...    207 


LIST  OF  EXPERIMENTS 

EXPERIMENT  PAGE 

1.  To  Study  the  Polarity  of  a  Magnet -.»:...  3 

2.  To  Study  the  Laws  of  Magnetic  Attraction 3 

3.  To  Study  the  Variation  of  Attraction  with  Distance 4 

4.  To  Study  a  Magnetic  Field 6 

5.  To  Study  the  Magnetic  Field  around  two  Bar  Magnets 9 

6.  To  Study  the  Molecular  Theory  of  Magnetism .  10 

7.  To  Study  Magnetic  Induction 13 

8.  To  Study  the  Effect  of  Heat  on  Magnetism 14 

9.  To  Study  Terrestrial  Magnetism 15 

10.  To  Study  the  Magnetic  Field  around  an  Electric  Wire 24 

11.  To  Study  the  Effect  of  an  Electric  Current  on  a  Magnetic  Needle  .  24 

12.  To  Study  the  Properties  of  Solenoids 25 

13.  To  Study  the  Development  of  Magnetism  in  an  Iron  Core      ...  33 

14.  To  Study  the  Magnetic  Properties  of  a  U-shaped  Bar 34 

15.  To  Study  the  Construction  and  Operation  of-  the  Electric  Bell   .    .  47 

16.  To  Study  the  Principles  of  the  Telegraph 48 

17.  To  Study  the  Principles  of  Telephone  Receivers 51 

18.  To  Study  Electromagnetic  Induction 65 

19.  To  Study  the  Development  of  an  E.M.F.  by  Electromagnets.    .    .  73 

20.  To  Study  the  Cause  of  Sparking  at  Break  in  an  Inductive  Circuit .  82 

21.  To  Study  the  Simple  Voltaic  Cell 89 

22.  To  Study  an  Electromotive  Force  or  Pressure 93 

23.  To  Study  Polarization ......  96 

24.  To  Study  the  Electromotive  Force  of  Different  Cells 100 

25.  To  Study  Electrolytic  Decomposition 105 

26.  To  Study  the  Principles  of  the  Storage  Cell Ill 

27.  To  Study  the  Relation  between  Length  of  Conductor  and  Current 

when  Pressure  is  kept  Constant 124 

28.  To  Study  the  Relation  between  the  Size  of  Wire  and  Current  when 

Pressure  is  kept  Constant 128 

29.  To  Study  the  Dependence  of  the  Resistance  of  a  Conductor  on  the 

Material  of  Which  it  is  Made 133 

30.  To  Study  the  Effect  of  Temperature  upon  the  Resistance  of  a 

Conductor 136 

31.  To  Verify  Ohm's  Law 144 

32.  To  Study  the  Resistance  of  Conductors  in  Series 150 

33.  To  Study  Voltage  Drop 152 

34.  To  Study  the  Resistance  of  Conductors  Connected  in  Parallel    .    .  156 

35.  To  Study  the  Pressure  of  Cells  Connected  in  Series 164 

36.  To  Study  the  Principles  of  the  Electric  Generator 172 

37.  To  Study  the  Relation  of  Induced  Electromotive  Force  to  Speed  .  176 

xiii 


xiv  LIST  OF  EXPERIMENTS 

EXPERIMENT  PAGE 

38.  To  Study  the  Relation  of  Induced  Electromotive  Force  and  Strength 

of  Magnetic  Field 177 

39.  To  Investigate  the  Cause  of  Rotation  of  Motor  Armature  ....  181 

40.  To  Determine  the  Direction  of  Rotation  of  Motor  Armature      .    .  183 

41.  To  Study  the  Relation  between  the  Strength  of  the  Magnetic  Field 

and  the  Speed  of  Rotation 183 

42.  To  Study  the  Separately  Excited  Motor 184 

43.  To  Study  the  Operation  of  a  Series  Motor 188 

44.  To  Study  the  Operation  of  a  Shunt  Motor 190 


ELEMENTARY  MAGNETISM 

AND 

ELECTRICITY 

CHAPTER  I 
MAGNETISM 

1.  Introduction. — The  subject  of  magnetism  and  electricity  is 
best  approached  from  the  experimental  side,  for  only  by  such 
means  will  the  interactions  of  magnetic  and  electric  forces  become 
real  to  the  student.     The  handling  of  the  apparatus,  together 
with  reports  upon  the  observed  phenomena,  is  about  the  only  way 
in  which  a  student  can  get  a  clear  understanding,  or  realizing 
sense,  of  electric  and  magnetic  principles.     Thus  the  generation 
of  an  electromotive  force  in  a  dynamo  is  merely  due  to  relative 
motion  between  a  magnetic  field  and  copper  wire,  and,  unless 
the  student  has  a  clear  notion  of  a  magnetic  field  and  the  inter- 
action between  conductor  and  field,  he  can  never  get  a  clear  under- 
standing of  the  fundamental  principle  of  all  dynamo-electric 
machinery.     We  shall  thus  begin  this  course  with  a  study  of 
magnetism  and  learn  why  magnets  are  important  industrially. 

2.  Magnetism. — The  essential  nature  of  the  property  called 
magnetism  is  unknown.     We   only  know  that   under  certain 
conditions  a  piece  of  iron,  or  steel,  acquires  the  property  of 
attracting  other  pieces  of  iron  by  a  force  which  is  many  times  as 
great  as  the  force  of  attraction  between  the  two  pieces  due  to 
gravity,  and  also  that  there  is  a  reaction  between  this  property 
and  a  like  property  of  the  earth  which  tends  to  cause  the  piece 
of  iron  to  assume  a  definite  position  with  reference  to  the  earth's 
meridian,  that  is,  a  north  and  south  line. 

By  magnetism  is  thus  meant  the  property  a  body  has  of  attract- 
ing iron  with  a  force  which  is  neither  gravitation  nor  due  to 
mechanical  action  of  ordinary  matter,  and  which  will  tend  to  set 
the  body  in  a  north  and  south  direction. 

1 


2  MAGNETISM  AND  ELECTRICITY 

This  definition  clearly  does  not  tell  us  much  about  magnetism, 
it  merely  enables  us  to  distinguish  between  magnetic  forces  and 
other  forces.  We  thus  recognize  a  magnet  by  its  action.  The 
fact  that  some  substances  possess  this  property  has  been  known 
for  centuries.  An  iron  ore  which  was  first  found  in  Magnesia 
(Asia  Minor)  was  first  observed  to  possess  this  property  and  from 
this  the  word  magnet  was  undoubtedly  derived.  This  iron  ore, 
commonly  called  lodestone,  which  means  attracting  stone,  has 
no  industrial  use  based  on  its  attracting  property. 

3.  Magnets. — A  body  possessing  the  property  of  magnetism  is 
called  a  magnet.  The  only  substance  of  which  commercial 
magnets  are  made  is  iron  or  some  of  its  forms,  although  there  are 
other  substances  that  can  be  magnetized.  To  this  class  belong 
nickel,  cobalt,  manganese,  and  an  interesting  alloy  named  after 
its  inventor  "Heusler's  alloy."  This  is  an  alloy  of  copper, 
manganese,  and  aluminum.  Recently  several  other  such  alloys, 


FIG.  1.  FIG.  2. 

all  containing  either  manganese  or  chromium,  have  been  found  to 
possess  magnetic  properties. 

4.  Permanent  and  Temporary  Magnets. — Before  the  discovery 
of  the  relation  between  magnetism  and  an  electric  current,  mag- 
nets were  made  by  stroking  the  lodestone  with  a  piece  of  iron. 
When  the  lodestone  was  touched  with  a  piece  of  iron  the  iron 
itself  acquired  the  property  of  attracting  other  pieces  of  iron,  or 
as  we  now  say  became  magnetized.  The  time  during  which  this 
property  of  attraction  was  retained  depended  upon  the  quality 
of  the  iron.  If,  upon  removal  from  contact  with  the  lodestone, 
the  iron  lost  most  of  its  magnetism,  it  was  called  a  temporary 
magnet.  A  piece  of  steel  which  was  hardened  before  magnetizing 
retained  its  magnetic  properties  indefinitely  and  accordingly 
was  called  a  permanent  magnet. 

Magnets  are  now  made  either  by  stroking  a  permanent  magnet 
in  one  direction  by  the  piece  of  steel  to  be  magnetized,  or  by 
passing  electric  currents  about  the  steel  bar  in  a  manner  to  be 
described  later. 


MAGNETISM 


3 


6.  Forms  of  Magnets. — Forms  of  commercial  magnets  are  too 
numerous  to  mention.  The  two  common  forms  of  permanent 
magnets  are  the  bar,  Fig.  1,  and  horseshoe,  Fig.  2. 

6.  Experiment  1.    Poles  of  a  Magnet. 
Apparatus. — 

Bar  magnet 

Iron  filings 

Operation. — Take  a  shallow  pasteboard  box,  like  a  thread  box, 
and  spread  the  iron  filings  over  the  bottom  of  it.  Take  one  of 
the  bar  magnets  and  lay  it  flat  upon 
the  iron  filings;  turn  the  magnet  over 
and  lift  it  from  the  box.  Do  the  iron 
filings  adhere,  or  stick,  to  all  parts  of 
the  magnet?  Draw  a  diagram  show- 
ing the  parts  to  which  the  iron  filings 
adhere.  The  parts  near  the  ends  of 
a  magnet  to  which  iron  filings  cling 
are  called  the  poles  of  the  magnet. 
Take  a  magnetic  needle  and  dip  it 
into  the  iron  filings  in  the  same  way. 
Does  it  too  have  poles?  Remove  the 
iron  filings  by  brushing  with  a  cloth 
Never  strike  the  magnet  to  dislodge 
the  iron  filings. 

7.  Experiment  2.    Laws  of  Mag- 
netic Attraction. 

Apparatus. — 

Two  bar  magnets 

Supporting    stirrup 

Operation. — Arrange  a  stirrup  of  wire  supported  by  an  un- 
twisted thread  as  indicated  in  Fig.  3.  Place  one  of  the  bar 
magnets  in  the  stirrup  and  note  which  end  points  north.  Mark 
this  end  -f  with  a  pencil  or  a  piece  of  chalk.  Replace  the  bar 
magnet  by  the  second  magnet  and  also  note  which  end  points 
north.  Now  take  bar  magnet  No.  1,  and  hold  the  +  end  near 
the  +  end  of  the  bar  magnet  in  the  stirrup.  Observe  carefully 
whether  there  is  an  attraction  or  repulsion  between  the  magnets. 
Repeat  this  several  times  until  you  are  certain  of  the  result. 
Reverse  the  bar  magnet  held  in  the  hand  and  repeat  the  experi- 
ment. Perform  the  same  experiment  with  the  other  end  of  the 
suspended  magnet.  Formulate  your  answers  like  this: 


FIG.  3. 


MAGNETISM  AND  ELECTRICITY 


Like  poles 


each  other. 


.       f  attract  \         ,       , 
Unlike  poles  <  j    >  each  other. 

Use  the  correct  word  attract  or  repel  in  each  case. 
8.  Experiment  3.     Variation  of  Attraction  with  Distance. 

Apparatus.  — 

Compass  needle 

Bar  magnet 

Operation.  —  It  will  be  impossible  to  get  exact  values  with  the 
simple  apparatus  at  hand,  but  an  idea  of  the  variation  of  the  force 
of  attraction  and  repulsion  may  be  obtained  if  this  experiment  is 
carefully  performed.  Place  the  mounted  compass  needle  and 
bar  magnet  in  the  relative  positions  shown  in  Fig.  4.  First  note 
and  record  the  reading  or  position  of  the  compass  needle  before 
the  magnet  is  brought  near.  After  placing  the  magnet  in  posi- 
tion, measure  the  distance  d  and  read  the  deflection  of  the  com- 
pass needle.  That  is,  through  what  angle  has  the  needle  been 
deflected?  If  the  original  position  of  the  ^V-end  was  on  0 
degrees  and  after  the  magnet  is  brought  near  it  is  20  degrees,  the 
deflection  is  20  degrees.  If,  however,  the  original  position  is 
10  degrees  and  second  position  20  degrees  the  deflection  is  only 
20  degrees  —  10  degrees  =  10  degrees.  Repeat  this  by  moving 
the  bar  magnet  farther  and  farther  from  the  compass.  Make 
observations  for  at  least  5  positions  of  the  bar  magnet.  Tabulate 
your  results  as  follows: 


Setting 

tf-Pole  near  AT-Pole 

d 

Deflection 

1 
2 
3 
4 
5 

9.  Theory. — The  results  of  this  experiment  will  not  give  the 
exact  variation  or  relation  between  deflection  and  distance 
between  magnet  poles.  In  the  first  place,  both  poles  of  the  bar 
magnet  influence  both  ends  of  the  compass  needle,  and  then  again 
the  relation  between  d  and  deflection  is  not  constant.  The  im- 
portant point  for  the  beginner  in  the  experiment  is  the  fact  that 
the  deflection  decreases  as  the  distance  d  increases.  Many 


MAGNETISM  5 

refined  experiments  have  been  performed  which  show  that  the 
force  of  attraction  or  repulsion  between  the  two  poles  decreases 
as  the  square  of  the  distance  between  them.  If  we  express  this 
relation  algebraically,  that  is  in  symbols,  we  get 

_  strength  of  one  pole  X  strength  of  other  pole 

square  of  distance  between  them 
OTF  _ 


where  mi  and  m2  are  pole  strengths  expressed  in  the  same  units 
and  d  is  the  distance  between  the  poles. 


FIG.  4. 

10.  Unit  Pole. — In  the  foregoing  expression,  the  letter  F 
stands  for  "force,"  but  in  what  units  this  force  is  measured  will 
depend  upon  the  assumed  unit  of  pole  strength.  The  results  of 
experiment  1  show  that  the  iron  filings  adhered  to  the  ends  of  the 
bar  magnet.  These  ends  are  usually  called  poles,  but  as  the  sur- 
face to  which  the  iron  filings  cling  is  quite  extended,  they  may  be 
called  distributed  poles.  The  definition  of  unit  pole  is  based  on 
the  assumption  that  all  of  the  magnetic  influence  is  concentrated 
upon  one  point.  Under  this  restriction  the  unit  pole  is  a  point 
pole  which  repels  with  a  force  of  one  dyne  an  equal  point  pole 
placed  1  cm.  away  in  air.  A  dyne  is  a  unit  of  force  and  is  approxi- 
mately about  1/980  of  a  gram,  or  1/445000  of  a  pound.  The 
force  exerted  by  two  unit  poles  is  thus  very  small.  The  force  of 
repulsion  or  attraction  between  two  magnet  poles  is  then  a  meas- 
ure of  the  magnetism  in  the  poles.  Thus,  if  one  of  the  poles  is  a 
unit  pole,  and,  when  another  pole  is  brought  near,  the  force  is 

200  dynes,  we  say  that  the  unknown  pole  contains  200  units  of 
2 


6  ,       MAGNETISM  AND  ELECTRICITY 

magnetism  or  has  200  unit-poles  strength.     The  centimeter  is  a 
unit  of  length  and  equals  0.3937  in. 

EXAMPLE 

Two  poles  of  10  and  15  units  strength  respectively  are  placed  at  a  distance 
of  15  cm.  apart.     What  is  the  force  between  them? 

Solution.  — 


m\  =  10  units 
m2  =  15  units 
d  =  15,  d2=225 


Hence,      F  =  ~          =  2/3  dynes. 

11.  Properties  of  Space  Surrounding  a  Magnet.  —  It  is  impor- 
tant to  know  whether  these  unique  properties  of  a  magnetized  bar 
are  confined  to  the  surface  of  the  bar,  or  whether  they  extend 
out  into  space,  and  if  the  influence  does  extend  into  space,  what 
are  some  of  its  characteristics.     This  problem  can  also  be  best 
investigated  by  experiment. 

12.  Experiment  4.    Magnetic  Field. 
Apparatus.  — 

Bar  magnet 

Horseshoe  magnet 

Iron  filings 

Several  sheets  of  paper 

Operation.  —  Place  one  of  the  bar  magnets  on  a  horizontal 
surface  and  upon  the  magnet  place  a  sheet  of  stiff  writing  paper 
or  a  piece  of  cardboard.  Arrange  the  paper  so  that  it  is  horizon- 
tal and  smooth.  Put  some  iron  filings  into  a  cheesecloth  bag 
and  sift  them  upon  the  paper,  tapping  the  paper  gently  while  the 
iron  filings  are  being  sifted.  Note  carefully  the  manner  in  which 
the  iron  filings  arrange  themselves.  Pour  the  iron  filings  back 
into  the  cheesecloth  bag  and  repeat  to  see  if  the  same,  or  nearly 
the  same,  configuration  of  iron  filings  can  be  reproduced.  If  so, 
take  another  sheet  of  paper  and  on  it  draw  an  outline  of  the  bar 
magnet.  On  this  same  sheet  draw  pencil  lines  representing  the 
arrangement  of  the  iron  filings. 

Another  method  of  obtaining  the  distribution  of  the  iron 
filings  is  to  place  upon  the  bar  magnet  a  pasteboard,  and  upon  the 
pasteboard  spread  smoothly  a  piece  of  blue-print  paper,  sensitized 
side  up.  Sprinkle  iron  filings  upon  the  blue-print  paper  as  before, 


MAGNETISM 


and  when  a  proper  pattern  has  been  obtained,  expose  the  blue- 
print paper  and  iron  filings  to  the  sun  for  two  or  three  minutes. 
Shake  off  the  iron  filings  in  a  dish  and  wash  the  blue-print  paper 
in  a  basin  of  water.  If  the  experiment  is  carefully  performed 
there  will  be  left  on  the  blue-print  paper  a  tracing  of  the  iron 
filings. 

13.  Theory. — This  experiment  shows  that  the  magnetic  influ- 
ence permeates  the  space  about  the  iron  bar.     The  space  around 
a  magnet  which  is  permeated  by  a  magnetic  influence  is  a  mag- 
netic field.     When  a  magnetic  substance,  such  as  the  iron  filings, 
is  placed  within  the  field, 

it  becomes  magnetized 
and  sets  itself  in  a  definite 
line.  The  iron  filings  be- 
come small  magnets,  and 
as  already  pointed  out, 
when  two  magnets  are 
brought  near  each  other 
a  force  is  exerted  between 
them.  This  force  causes 
the  iron  filings  to  make 
certain  designs  as  shown 
in  Fig.  5.  This  represen- 
tation of  a  magnetic  field 
is  only  in  one  plane,  that 
is,  in  the  plane  of  the  pa- 
per which  was  laid  on  the  bar  magnet.  A  similar  design  will  be 
obtained  if  the  magnet  is  turned  on  edge  or  in  any  position  par- 
allel to  its  length.  This  means  that  the  magnetic  field  com- 
pletely surrounds  the  bar  magnet  and  is  carried  with  it  when 
the  magnet  is  moved. 

14.  Unit  Magnetic  Field. — Just  as  the  strength  of  a  magnetic 
pole  is  measured  by  the  force  it  exerts  on  a  unit  magnetic  pole, 
the  strength  of  a  magnetic  field  is  defined  in  terms  of  the  force  it 
will  exert  upon  a  unit  magnet  pole.     If  a  small  compass  be  placed 
on  the  paper  above  the  bar  magnet,  the  magnetic  needle  will  lie 
parallel  or  be  tangent  to  the  lines  as  shown  in  Fig.  6.     The  north 
pole  of  the  compass  needle  is  pulled  in  one  direction  and  the  south 
pole  in  the  opposite  direction.     The  magnetic  field  thus  exerts  a 
force  upon  the  magnetic  needle.     If  it  were  possible  to  isolate  a 
north  pole  and  place  it  on  the  plane  of  the  paper  it  would,  if  free, 


FIG.  5. 


8  MAGNETISM  AND  ELECTRICITY 

move  from  the  north  pole  of  the  bar  magnet  toward  the  south  pole. 
This  force  that  a  magnetic  field  is  capable  of  exerting  upon  a 
magnet  pole  is  used  to  define  the  field  strength,  a  unit  field  being 
defined  as  follows: 

A  magnetic  field  of  unit  strength  is  one  which  is  capable  of 
exerting  a  force  of  one  dyne  upon  a  unit  magnet  pole.  The  unit 
of  magnetic  field  strength  or  intensity  is  called  the  gauss  after 
the  famous  German  physicist  and  mathematician. 

15.  Representation  of  a  Magnetic  Field. — Since  the  iron 
filings  are  arranged  in  lines  or  rows,  it  is  customary  in  practice  to 
speak  of  the  magnetic  field  as  consisting  or  being  composed  of 
lines,  and  the  strength  of  field  is  then  represented  by  the  number 


FIG.  6. 

of  lines  per  square  centimeter  or  per  square  inch,  in  a  plane  at 
right  angles  to  the  magnetic  field.  A  field  of  unit  strength  is 
then  represented  by  one  line  per  square  centimeter,  and  a  field 
of  ten  units  by  ten  lines,  etc.  The  student  must  remember,  how- 
ever, that  this  is  merely  a  method  of  representing  a  magnetic  field. 
The  magnetic  field  occupies  or  permeates  all  of  the  space  near  and 
around  a  bar  magnet.  Usually  the  field  is  not  of  uniform  strength 
at  every  point,  but  there  is  no  point  in  the  space  around  the  mag- 
net entirely  free  from  a  magnetic  field.  The  ether  surrounding 
a  bar  magnet  is  not  fibrous  like  a  muscle;  the  system  of  lines  is 
used  merely  for  convenience  in  making  calculations,  and  the 
development  of  the  electro-magnetic  theory. 


MAGNETISM 


9 


16.  Experiment  5.     Magnetic  Field  around  two  Magnets. 

Apparatus. — 

Two  bar  magnets 

Iron  filings 

Paper 

Operation. — This  experiment  is  performed  exactly  in  the  same 
manner  as  experiment  4.  The  two  bar  magnets  are  placed  on  a 
horizontal  surface,  parallel  to  each  other,  and  about  1  in.  apart. 
First  place  unlike  poles  near  each  other  and  sprinkle  iron  filings 
upon  the  paper  as  before.  Draw  a  diagram  showing  the  arrange- 
ment of  the  iron  filings.  Do 
the  bar  magnets  attract  or 
repel  each  other? 

Next  reverse  one  of  the 
bar  magnets  and  repeat. 
Again  draw  a  diagram  show- 
ing the  distribution  and  ar- 
rangement of  lines.  Com- 
pare this  with  the  previous 
diagram.  What  differences 
are  observed  ?  In  which  case 
is  there  an  attraction?  In 
which  case  is  there  a  repul- 
sion between  the  magnets? 

17.  Theory. — An  examin- 
ation  of   the    diagrams  ob- 
tained from  experiment  5  will  FIG.  7. 
show  that  when  the  unlike 

poles  are  near  each  other  the  iron  filings  are  arranged  in  lines 
extending  from  one  pole  of  one  magnet  to  the  near  pole  of  the 
other  magnet.  We  say  that  the  magnetic  lines  pass  from  one 
magnet  pole  to  the  adjacent  pole  of  the  other  magnet. 

The  other  diagram  shows  that  when  like  poles  are  near,  the 
lines  from  one  magnet  do  not  enter  the  other  magnet,  but  are 
pushed  aside.  In  the  first  case  the  tension  along  the  lines  tends 
to  draw  the  bar  magnets  near  each  other  while  in  this  case  there 
is  manifest  a  force  of  repulsion.  Although  this  does  not  fully 
explain  why,  it  shows  that  unlike  poles  attract  and  like  poles 
repel.  Figs.  7  and  8  show  the  characters  of  the  magnetic  fields 
between  unlike  and  like  poles  when  the  bar  magnets  are  placed 
end  to  end. 


10 


MAGNETISM  AND  ELECTRICITY 


18.  Magnetism  a  Molecular  Property. — Although  the  exact 
relation  between  the  property  called  magnetism  and  the  physical 
structure  of  a  magnetic  substance  is  not  known  in  detail,  a  theory 
which  helps  in  the  understanding  of  certain  well-known  phe- 
nomena has  received  almost  universal  acceptance.  The  elements 
of  this  theory  will  be  brought  out  by  the  following  experiment. 


FIG.  8. 


19.  Experiment  6.    Molecular  Theory  of  Magnetism. 

Apparatus. — 

Compass 

Bar  magnet 

Sewing  needle 

Iron  filings 

Small  round  bottle  or  test  tube 

Operation. — Fill  the  small  bottle  with  iron  filings  and  test 
for  polarity.  That  is,  first,  hold  one  end  of  the  bottle  near  the 
north  pole  of,  and  at  right  angles  to,  the  magnetic  needle.  Turn 
the  bottle  end  for  end,  and  again  test.  Does  the  bottle  act  as  a 
bar  magnet  or  as  an  unmagnetized  piece  of  iron? 

Next  stroke  the  bottle  with  one  end  of  a  bar  magnet  from  end 
to  end  as  indicated  in  Fig.  9.  Without  shaking  or  jarring  the 
iron  filings,  again  test  for  polarity.  Have  magnetic  poles  been 
developed?  Shake  the  bottle  so  as  to  disarrange  the  iron  filings 


MAGNETISM 


11 


and  again  test  for  polarity.  Repeat  this  process  until  you  are 
certain  of  your  results. 

Take  a  large,  unmagnetized  sewing  needle  and  dip  it  into  iron 
filings;  no  filings  will  cling  to  it.  Magnetize  the  needle  by  strok- 
ing it  from  one  end  to  the  other  with  one  pole  of  the  bar  magnet; 
dip  it  into  the  filings  again  and  observe  that  the  filings  adhere 
near  the  ends  of  the  needle.  Break  the  magnetized  needle  and 
dip  the  pieces  into  the  filings.  Do  the  filings  adhere  to  the  ends 
of  the  pieces?  Are  the  pieces  also  magnets?  Break  one  of  the 
pieces  in  two  and  repeat. 
Are  the  small  pieces  mag- 
nets? Test  each  piece  for 
polarity. 

20.  Theory. — The  theory 
of  the  physical  structure  of 
bodies  is  to  the  effect  that 
if  it  were  possible  to  con- 
tinue the  subdivision  indefi- 
nitely, we  should  obtain 
ultimately  a  particle  which 
was  incapable  of  further 
subdivision  by  mechanical 
means,  such  as  grinding, 
dissolving,  etc.  If  we  use 
chemical  means  to  further 
subdivide  the  particle  the  FIG.  9. 

kind  of  matter  is  changed. 

Either  the  particle  is  decomposed  into  simple  substances,  or  com- 
bined with  other  substances,  but  in  either  case  it  no  longer  has 
the  same  properties.  This  mechanically  indivisible  particle  is  a 
molecule  and  all  bodies  are  supposed  to  consist  of  molecules. 

The  experimental  facts  concerning  the  magnetic  properties  of 
small  pieces  of  iron  or  steel  point  to  the  conclusion  that  the  ar- 
rangement of  the  molecules  has  something  to  do  with  magnetism, 
for  when  the  iron  filings  were  in  a  jumbled  mass  no  external 
magnetism  was  apparent.  When  the  bottle  was  subjected  to  a 
magnetic  influence  the  iron  filings  assumed  definite  positions 
and  the  whole  mass  developed  poles.  A  sudden  violent  dis- 
turbance, however,  weakened  or  destroyed  this  magnetism. 

The  process  of  breaking  the  smaller  pieces  of  the  needle  in 
two  can  be  continued  indefinitely  and  after  each  division  it  will 


12 


MAGNETISM  AND  ELECTRICITY 


be  found  that  the  pieces  are  magnets.     A  careful  test  by  the 
student  will  show  that  this  is  well  illustrated  by  Fig.  10. 

To  explain  this  phenomena  it  is  assumed  that  the  molecules 
are  themselves  small  magnets,  and  that  ordinarily  they  are  ar- 
ranged in  closed  magnetic  circuits  within  the  bar.  When,  how- 
ever, the  bar  is  subjected  to  a  magnetizing  force,  the  molecules 
are  forced  to  arrange  themselves  in  such  a  way  that  the  N-poles 
point  in  one  direction  and  the  $-poles  in  the  opposite  direction. 


FIG.  10. 

Under  such  an  arrangement  the  opposite  poles  of  the  molecules 
neutralize  each  other  in  the  bar  of  iron,  but  at  the  ends  the  poles 
are  exposed  and  the  magnetic  influence  extends  into  surrounding 
space.  This  theory  is  illustrated  in  Figs.  11,  12,  and  13.  The 
supposed  arrangement  of  molecules  of  an  unmagnetized  bar  is 
shown  in  Fig.  11.  The  molecules  are  represented  by  small 
rectangles,  and  opposite  poles  by  light  and  shaded  portions. 


FIG.  11. 

As  is  shown,  the  molecules  are  arranged  in  a  haphazard  way  but 
forming  closed  magnetic  circuits. 

In  Fig.  12  the  molecules  are  shown  in  a  more  symmetrical 
arrangement,  but  not  all  pointing  in  the  same  direction.  This 
would  represent  the  condition  in  a  bar  magnetized,  but  not  to 
its  greatest  possible  value.  In  Fig.  13  all  the  molecules  are  shown 
as  pointing  in  the  same  direction  and  under  these  conditions  the 
bar  is  said  to  be  a  saturated  magnet.  The  student  must  remem- 


MAGNETISM  13 

ber  that  there  is  no  absolute  proof  that  these  conditions  actually 
exist  as  here  represented.  The  theory  explains  the  phenomena 
better  than  any  other  so  far  proposed.  Likewise,  the  reader 
must  not  suppose  that  molecules  are  rectangular  in  cross-section. 
What  shapes  molecules  may  have  no  one  knows. 

21.  Magnetic  Induction. — The  change  produced  in  the  arrange- 
ment of  the  molecular  magnets  when  in  the  presence  of  a  magnet 
or  under  the  influence  of  a  magnetic  field  is  called  magnetic 


FIG.  12. 

induction.     The  next  experiment  will  show  that  only  some  sub- 
stances can  be  magnetized  by  induction. 
22.  Experiment  7.     Magnetic  Induction. 
Apparatus. — 
Bar  magnet 
Nails 

Piece  of  copper  wire 
Match 
Iron  filings 


FIG.  13. 

Operation. — Dip  the  point  of  a  nail  into  iron  filings  and  notice 
if  any  filings  adhere,  or  cling  to  it,  when  it  is  withdrawn.  Again 
dip  the  point  of  the  nail  into  the  filings,  and  while  in  this  position 
hold  one  end  of  the  bar  magnet  against  the  head  of  the  nail. 
Do  the  iron  filings  adhere  to  the  point  of  the  nail  while  the  magnet 
is  touching  the  head?  Remove  the  bar  magnet  and  see  if  as 
many  filings  cling  to  the  point.  Why?  Repeat  this  by  using  a 


14 


MAGNETISM  AND  ELECTRICITY 


copper  wire,  a  match,  a  glass  rod  in  place  of  the  nail.     What  do 
you  learn? 

23.  Theory. — Touching  the  nail  made  a  temporary  magnet  of 
it,  or  in  other  words,  developed  magnetic  properties  within  it. 
The  development  of  magnetism  within  a  body  when  placed  in  the 
vicinity  of  a  magnet  is  called  magnetic  induction.  Magnetism 
is  said  to  have  been  induced  in  the  nail  when  it  was  touched  with 
the  bar  magnet.  When  the  bar  magnet  was  removed  from  con- 
tact with  the  nail,  most  of  the  magnetism  disappeared;  the  small 
amount  that  remained  is  called  residual  magnetism.  This 
residual  magnetism  is  usually  sufficient  to  supply  the  initial 
excitation  in  electrical  generators. 


FIG.  14. 

The  experiment  also  shows  that  magnetism  can  be  induced  in 
iron,  but  not  in  copper,  wood  or  glass.  Substances  in  which 
magnetism  can  be  induced  are  called  magnetic,  or  para-magnetic. 
Those  in  which  magnetism  cannot  be  induced  are  called  non- 
magnetic. There  is  still  another  class  of  bodies  which  when 
brought  near  a  bar  magnet  are  repelled.  Bismuth  is  the  best 
example  of  this  class. 

24.  Experiment  8.    Effect  of  Heat  on  Magnetism. 
Apparatus. — 

A  gas  burner  or  lamp  (an  alcohol  lamp  is  best) 
Nail 

Bar  magnet 
Operation. — Suspend  a  small  nail  by  means  of  a  thin  wire,  as 


MAGNETISM  15 

shown  in  Fig.  14.  Heat  the  nail  to  red  heat  and  bring  the  bar 
magnet  near  it.  Does  the  bar  magnet  attract  the  nail?  Re- 
move the  lamp,  and  after  the  nail  has  cooled  again  test  it  for 
magnetism.  Does  the  nail  regain  its  magnetic  properties? 

Magnetize  a  sewing  needle  and  then  heat  it  to  redness,  and 
dip  the  needle  after  heating  into  iron  filings.  Is  the  needle 
still  a  magnet? 

25.  Theory. — According  to  the  molecular  theory  of  magnetism, 
the  development  of  magnetism  is  explained  on  the  assumption 
that  the  particles  of  iron  are  turned  under  the  influence  of  the 
magnetizing  field.     The  iron  itself  becomes  for  the  time  being  a 
magnet,  or  magnetism  is  induced  in  the  iron.     At  red  heat,  iron 
loses  its  magnetic  quality.     This  means  not  only  that  a  magnet 
may   be  demagnetized  by  being  heated  to  about  800  degrees 
Centigrade,  but  also  that  iron,  when  heated  to  this  tempera- 
ture, is  no   longer   capable    of    being    attracted    by  a  magnet. 
On  cooling,  however,  the  iron  regains  its  magnetic  quality  at  a 
somewhat  lower  temperature. 

According  to  the  kinetic  theory  of  matter  all  molecules  are 
supposed  to  be  in  motion.  This  motion  is  greatly  increased  by 
heat;  hence,  heating  a  magnet  will  cause  the  molecules  to  move 
so  rapidly  that  they  cannot  be  kept  " lined  up"  by  the  influence 
of  the  magnetic  field. 

26.  Magnetism  of  the  Earth. — The  fact  that  there  is  a  magnetic 
field  around  the  earth  is  well  shown  by  the  behavior  of  a  magnetic 
needle.     The  presence  and  influence  of  this  field  is  not  always 
realized.     The  following  experiment  will  aid  greatly  in  under- 
standing this  influence. 

27t  Experiment  9.    Terrestrial  Magnetism. 
Apparatus. — 

Mounted  magnetic  needle 
About  2  ft.  of  3/4-in.  or  1-in.  gas  pipe 
Hammer 

Operation. — First  test  the  piece  of  gas  pipe  for  magnetism  by 
holding  one  end  of  the  gas  pipe  near  the  TV-pole  of  a  magnetic 
needle  and  observe  whether  the  magnetic  needle  is  attracted  or 
repelled.  Reverse  the  pipe  and  test  the  other  end.  If  both  ends 
of  the  gas  pipe  attract  the  magnetic  needle,  the  gas  pipe  is  not 
magnetized  and  the  rest  of  the  experiment  may  be  performed. 

Hold  the  gas  pipe  in  the  left  hand  in  a  north  and  south  position, 
the  north  end  dipping  downward.  While  in  this  position  hit  the 


16  MAGNETISM  AND  ELECTRICITY 

pipe  several  hard  blows  with  the  hammer  and  again  test  the  pipe 
for  magnetism  as  before.  Is  the  pipe  a  magnet,  that  is,  does  one 
end  of  the  pipe  attract  and  the  other  end  repel  the  needle?  Can 
you  explain  this? 

Turn  the  gas  pipe  end  for  end  and  again  hold  it  in  a  north  and 
south  position  as  before  and  hit  it  several  more  blows  with  the 
hammer.  Test  for  magnetism  as  before  and  notice  if  the  end 
of  the  pipe  that  formerly  attracted  the  N-end  of  the  needle  still 
attracts  it.  Make  all  your  tests  with  the  ./V-pole  of  the  mag- 
netic needle.  If  you  find  the  magnetism  of  the  gas  pipe  has 
been  reversed,  explain. 

28.  Theory. — That  the  compass  needle  pointed  in  an  approxi- 
mately north  and  south  direction  was  known  in  the  time  of 
Columbus.  It  was,  however,  in  1860  that  Dr.  William  Gilbert, 
physician  to  Queen  Elizabeth,  first  explained  the  behavior  of  the 
compass  needle  by  the  assumption  that  the  earth  itself  is  a  mag- 
net with  a  south  pole  near  the  geographical  north  pole,  and  a 
north  pole  near  the  geographical  south  pole.  The  correctness 
of  this  assumption  has  since  been  completely  verified.  The  earth 
is  thus  surrounded  by  a  magnetic  field  in  exactly  the  same  man- 
ner as  the  bar  magnet  that  has  been  used  in  the  preceding  experi- 
ments. This  field  is  quite  weak  but  it  controls  the  magnetic  needle 
when  it  is  free  to  swing.  Furthermore,  it  was  shown  that  when 
a  nail  or  other  non-magnetized  body  is  subjected  to  the  influence 
of  a  bar  magnet,  it  (the  nail)  becomes  magnetized.  In  exactly 
the  same  way,  when  an  un-magnetized  body  is  subjected  to  the 
earth's  magnetic  field  it,  too,  will  become  magnetized.  On 
account  of  its  weakness,  the  earth's  field  will  not  magnetize  a 
body  so  readily  or  to  the  same  degree  as  the  bar  magnet.  In 
the  preceding  experiment,  when  the  piece  of  pipe  is  held  in  a 
north  and  south  position  with  the  north  end  dipping  below  the 
horizon,  it  is  approximately  in  the  same  direction  as  the 
earth's  magnetic  field.  The  magnetic  field  of  the  earth  attempts 
to  "line  up"  the  molecules  but  without  help  it  is  too  weak  to 
have  any  permanent  effect.  When  the  gas  pipe  is  suddenly 
jarred,  as  when  it  is  hit  with  the  hammer,  the  force  exerted  by 
the  earth's  field  is  sufficiently  strong  to  align  enough  of  the  mole- 
cules so  that  the  pipe  behaves  as  a  magnet.  It  is  thus  magnetized 
by  the  action  of  the  earth's  magnetic  field.  When  the  pipe  is 
reversed  the  influence  of  the  earth's  field  is  exerted  in  the  oppo- 
site direction  and  its  magnetism  is  reversed. 


MAGNETISM  17 

Any  one  working  in  a  machine  shop  has  undoubtedly  observed 
that  tools  become  magnetized.  A  good  example  is  the  vertical 
drill  to  which  the  chips  cling  when  it  is  withdrawn  from  the  hole 
being  drilled. 

29.  Declination. — The  earliest  users  of  the  compass  were  aware 
that  it  did  not  point  exactly  north  and  south,  but  it  was  Columbus 
who,  on  his  first  voyage,  discovered  that  the  compass  needle  did 
not  point  in  the  same  direction  at  all  points  on  the  earth's  surface. 
The  chief  reason  for  this  deviation  from  a  true  north  and  south 
direction  is  the  fact  that  the  earth's  magnetic  poles  do  not  coin- 
cide with  the  geographic  poles.  There  are,  however,  other  causes, 
such  as  large  deposits  of  iron  ore,  etc.  The  angle  which  the  needle 


FIG.  15. 

makes  with  the  meridian  at  any  place  is  called  the  declination 
at  that  place.  In  making  land  surveys  with  a  compass  the  declina- 
tion must  be  taken  into  account. 

30.  Dip. — If  an  unmagnetized  bar  be  suspended  so  that  it  is  in 
a  horizontal  position  and  then  magnetized  it  will  be  found  that 
it  no  longer  remains  horizontal.  In  the  northern  hemisphere 
the  north  seeking  end  will  dip  below  the  horizon.  This  shows 
that  the  earth's  field  is  not  horizontal  but  dips  toward  the  north. 
This  is  the  reason  why  the  gas  pipe  should  be  held  with  the  north 
end  lower  than  the  south  end  when  it  is  struck  with  the  hammer. 
The  angle  between  the  horizontal  and  the  direction  of  magnetic 
lines  is  called  the  angle  of  dip.  In  the  latitude  of  Madison  this 
angle  is  about  73°. 


18 


MAGNETISM  AND  ELECTRICITY 


31.  Practical  Uses  of  Permanent  Magnets. — The  earliest  use 
of  the  permanent  magnet  was  to  determine  direction,  that  is,  as  a 

compass  needle.  It  is  still  very  exten- 
sively used  for  this  purpose,  both  on  land 
and  sea.  For  land  use,  the  needle  usu- 
ally is  in  the  form  of  a  slim  bar  magnet 
pivoted  on  a  jewel  bearing  at  the  middle. 
One  form  of  surveyor's  compass  is  shown 
in  Fig.  15. 

A  mariner's  compass  is  made  in  a 
somewhat  different  form.  The  points  of 
the  compass  and  the  circle  divisions  are 
printed  on  a  paper  ring  which  is  attached 
to  a  light  aluminum  rim.  Radial  threads 
connect  the  ring  to  a  central  disk  which 
contains  a  sapphire  cap  by  which  the 
dial  is  supported  on  an  iridium  point. 
Eight  small  magnets  of  glass-hard  steel 
are  tied  to  the  radial  thread,  four  on 
each  side  of  the  jewel  cap.  The  direc- 
tive force  is  thus  due  to  the  action  of 
the  earth's  magnetic  field  upon  the  small 
magnets. 

Another  important  use  of  the  permanent  magnet  is  in  the  tele- 
phone receiver.  This  also  has  several .  forms,  one  of  which  is 
shown  in  Fig.  16.  As  shown  in  the  figure  the  yoke  consists  of  a 


FIG.  16. 


-V- 


II LI        l'_  --U--J 

i a iL__n__ 


Tf 


FIG.  17. 

piece  of  soft  iron  bent  into  the  horseshoe  form.     To  the  end  of 
this  are  attached  steel  pole  pieces.     Surrounding  the  pole  pieces 


MAGNETISM 


19 


are  two  coils  of  fine  wire.  Permanent  magnets  are  used  in  tele- 
phone receivers  for  two  reasons:  In  the  first  place,  they  give  a 
more  positive  and  stronger  action  to  the  diaphragm,  and  in  the 
second  place,  if  they  were  not  used  the  sound  at  the  receiver 


FIG.  18. 

would  be  an  octave  higher  than  that  at  the  transmitter  causing  it. 
Unscrew  the  cap  from  the  telephone  receiver  supplied  with  the 
apparatus  and  examine  its  construction.  Replace  the  diaphragm 
by  a  sheet  of  paper  and  sprinkle  iron  filings  over  it  so  as  to  deter- 
mine the  magnetic  field. 


FIG.  19. 


Permanent  magnets  of  the  horseshoe  form  are  also  used  on  the 
magneto  ringer  as  well  as  magneto  generator  used  on  automobiles 
for  ignition.  The  telephone  magneto  ringer  is  shown  in  Fig.  17. 

The  operation  of  nearly  all  forms  of  direct-current  measuring 


20  MAGNETISM  AND  ELECTRICITY 

instruments  depends  upon  the  interaction  between  the  magnetic 
field  of  a  permanent  magnet,  and  the  magnetic  field  due  to  a 
current.  Likewise  the  retardation  of  energy  meters  is  nearly 
always  due  to  the  action  of  horseshoe  magnets  of  the  permanent 
type.  The  form  of  magnet  employed  in  measuring  instruments 
is  shown  in  Fig.  18,  and  the  drag  magnets  of  a  watthour  meter 
are  shown  in  Fig.  19.  Magnets  intended  for  use  in  measuring 
instruments  must  not  change  in  strength  appreciably  with  time. 
They  must  not  only  be  magnetized  to  a  high  degree,  but  must 
also  retain  their  magnetism  indefinitely 

Another  interesting  use  of  magnets  is  for  the  removal  of  iron 
filings  from  the  eye  or  other  places  where  they  may  have  accident- 
ally lodged.  A  more  extended  discussion  of  the  uses  of  magnets 
will  be  given  after  electromagnetism  is  studied. 

RECAPITULATION 

1.  Magnetism  is  the  name  of  an  assumed  substance  producing  attrac- 
tion or  repulsion  between  pieces  of  iron  by  action  at  a  distance. 

2.  Magnets  are  bodies  possessing  the  property  of  magnetism.     Com- 
mercial magnets  are  made  exclusively  of  iron.    Permanent  magnets 
are  made  of  hardened  steel  and  retain  their  magnetism  indefinitely. 
Temporary  magnets  are  made  of  soft  iron  or  soft  steel  and  retain 
their  magnetism  only  so  long  as  they  are  subjected  to  a  magnetic 
influence. 

3.  The  poles  of  a  magnet  arc  the  ends  or  points  at  which  the  mag- 
netism is  concentrated. 

4.  The   laws   of  magnetic   attraction   are:    (a)   Like   poles  repel  and 
unlike  poles  attract,     (b)  The  forces  of  attraction  or  repulsion  are 
proportional  directly  to  the  product  of  the  pole  strengths  and 
inversely  as  the  square  of  the  distance  between  them. 

5.  The  strength  of  a  magnetic  pole  is  the  quantity  of  magnetism  at  the 
poles.    It  is  measured  by  the  force  the  magnet  pole  exerts  upon  a 
unit  pole. 

6.  Unit  pole  strength  or  a  unit  pole  is  that  pole  strength  which  repels  a 
like  pole  of  equal  strength  at  a  distance  of  1  cm.  in  air,  with  a 
force  of  one  dyne.     A  dyne  is  approximately  equal  to  1/445000 
Ib.  avoirdupois. 

7.  A  magnetic  field  is  the  region  or  space  which  is  permeated  by  a  mag- 
netic influence. 

8.  A  unit  magnetic  field  is  one  which  is  capable  of  exerting  a  force  of 
onq  dyne  upon  a  unit  magnet  pole. 

9.  The  strength  of  a  magnetic  field  is  usually  represented  graphically 


MAGNETISM  21 

by  the  number  of  lines  per  square  centimeter  in  a  plane  at  right 
angles  to  the  field. 

10.  According  to  the  molecular  theory  of  magnetism,  every  molecule  of 
a  piece  of  a  magnetic  substance  is  a  magnet.     When  the  magnetic 
body  is  neutral,  that  is,  has  no  magnetic  field  of  its  own,  the  mole- 
cules are  assumed  to  be  arranged  either  haphazard  or  in  little  closed 
groups  or  chains,  so  that,  on  the  whole,  opposite  poles  neutralize 
each  other  throughout  the  bar.     When,  however,  the  magnetic 
substance  is  subjected  to  a  magnetic  influence,  the  small  molecular 
magnets  are  lined  up,  the  north  and  south  poles  pointing  in  oppo- 
site directions. 

11.  Magnetic  induction  is  the  process  of  developing  magnetism  within 
a  magnetic  body  by  introducing  it  into  a  magnetic  field. 

12.  The  earth  has  magnetic  properties  like  a  bar  magnet. 

13.  Declination  is  the  name  given  to  the  angle  a  compass  needle  devi- 
ates from  a  true  north  and  south  line. 

14.  Dip  is  the  name  given  to  the  angle  the  earth's  magnetic  field  at  any 
point  makes  with  the  horizontal. 

15.  Permanent  magnets  have  many  practical  uses.     Some  of  the  most 
common   are   for   compass   needles,    electrical   meters,    telephone 
receivers,  etc. 


CHAPTER  II 
ELECTROMAGNETISM 

32.  Introduction. — In  the  first  chapter  we  learned  that  the 
space  surrounding  a  permanent  magnet  possesses  unique  proper- 
ties. Some  of  these  properties  became  apparent  when  iron  filings 
were  sprinkled  upon  paper  placed  on  the  magnet.  Other  prop- 
erties became  apparent  when  a  compass  needle  was  brought  near, 
and  when  the  magnet  was  suspended  so  as  to  swing  freely  in  a 
horizontal  plane.  It  will  be  interesting  to  learn  some  of  the  prop- 


c  z    c  z 

m 


FIG.  20. 

erties  of  wires  carrying  currents.  The  definition,  determination, 
and  laws  of  the  electric  current  will  be  taken  up  later.  At 
present  we  are  concerned  only  with  the  properties  of  a  current- 
bearing  wire  and  the  space  near  it  when  the  wire  is  connected  to 
the  binding  posts  of  an  electrical  cell,  such  as  a  dry  cell,  or  other 
source  of  current.  For  brevity  we  shall  call  a  wire  along  which 
an  electric  current  is  flowing,  an  electric  wire. 
4  23 


24  MAGNETISM  AND  ELECTRICITY 

33.  Experiment  10.     Magnetic  Field  around  an  Electric  Wire. 
Apparatus. — 

A  piece  of  cardboard 

Three  dry  cells 

Iron  filings 

Operation. — Connect  three  dry  cells  in  series;  that  is,  with  a 
short  piece  of  copper  wire  connect  the  carbon  rod  in  the  center  of 
one  cell  with  the  zinc  cup  of  the  next  cell,  etc.,  as  shown  in  Fig.  20. 
Arrange  your  apparatus  so  that  part  of  the  connecting  wire  AB 
shall  pass  through  a  piece  of  cardboard  in  a  vertical  direction. 
The  cardboard  must  be  horizontal.  It  is  also  advisable  to  have 

a  key  or  switch  K  in  the  circuit. 

_,  Hold  the  cardboard  in  a  hori- 

"  " 

zontal  position  and  sprinkle  some 

fine  iron  filings   upon  it.     Iron 
filings    that    have    been    sifted 
through  a  cheesecloth  will  work 
FIG.  21.  best.    Close  the  key  K  and  gently 

tap    the    paper.      Repeat    this 

several  times  and  draw  a  sketch  of  the  arrangement  of  the  iron 
filings  around  the  wire.  Next  remove  the  paper  and  dip  the 
electric  wire  in  some  iron  filings.  What  do  you  observe  upon 
removing  the  wire  from  the  iron  filings?  Do  any  iron  filings 
adhere  to  the  wire? 

34.  Experiment  11.    Effect  of  Electric  Current  upon  a  Mag- 
netic Needle. 

Apparatus. —     .    ••• 

Mounted  magnetic  needle  or  compass 

Dry  cell 

Operation. — Connect  the  two  binding  posts  of  the  dry  cell  by 
a  copper  wire  and  hold  the  wire  above  a  magnetic  needle  as  shown 
in  Fig.  21.  It  is  conventionally  assumed  that  the  current  leaves 
the  dry  cell  at  the  carbon  terminal  and  enters  at  the  zinc  cup. 
These  are  called  positive  and  negative  electrodes,  respectively. 
Hold  the  wire  above  the  needle  so  that  the  current  flows  along 
the  wire  from  south  to  north  and  note  carefully  the  direction  of 
the  deflection  of  the  needle.  Hold  the  wire  under  the  needle  and 
let  the  current  flow  from  north  to  south,  and  next  hold  it  so  that 
the  current  flows  from  south  to  north.  In  each  case  notice  and 
record  the  direction  of  deflection  of  the  north  seeking  end  of  the 
needle.  Finally,  hold  the  wire  in  a  vertical  position  in  front  of 


ELECTROMAGNETISM 


25 


the  north  seeking  pole  of  the  needle  and  observe  the  direction 
of  deflection  when  the  current  flows  downward,  and  again  when 
it  flows  upward.  Repeat  this  experiment  several  times  until 
the  principles  are  thoroughly  understood.  Record  your  observa- 
tions as  follows: 


Position  of  wire 

Direction  of  current 

Direction  of  deflection 

Below 

N  to  S 

West 

etc  

etc  

etc  

35.  Experiment  12.    To  Study  Solenoids. 

Apparatus. — Same  as  in  experiment  11. 

Operation. — With  the  apparatus  is  furnished  a  long  coil  of 
insulated  wire.  Connect  the  ends  of  this  coil  to  a  dry  cell,  as 
shown  in  Fig.  22.  Hold  one  end  of  this  coil,  which  is  called  a 
solenoid,  near  the  north 
seeking  pole  of  a  magnetic 
needle.  Is  the  needle 
attracted  or  repelled? 
Bring  the  other  end  of  the 
solenoid  near  the  same  pole. 
Does  the  needle  move  to- 
ward or  away  from  the  sole- 
noid? Try  the  experiment 
several  times  until  you  are 
certain  that  the  magnetic 
needle  is  always  deflected 
in  the  same  direction  when 
conditions  are  the  same. 

Change  the  solenoid  and 
battery  connections  and 
again  bring  the  ends  of  the  solenoid  near  the  compass  needle. 
Observe  carefully  whether  the  compass  needle  is  again  attracted 
or  repelled  by  the  same  end  that  attracted  or  repelled  it  before 
connections  were  reversed.  Can  you  account  for  this? 

Examine  carefully  the  connections  of  the  solenoid  and  note 
the  direction  in  which  the  current  flows  when  the  needle  is 
attracted  and  again  when  repelled.  Draw  a  solenoid  and  mark 
on  it  the  direction  of  current  flow  and  north  and  south  poles. 

36.  Theory. — The  three  preceding  experiments  are  very  im- 
portant, for  they  show  that  current-bearing  wire  has  all  of  the 


FIG.  22. 


26  MAGNETISM  AND  ELECTRICITY 

properties  of  a  magnet.  In  experiment  10  the  student  learned 
that  the  iron  filings  were  arranged  in  circles  around  the  wire. 
The  cardboard  really  forms  a  cross-section  of  the  field,  and 
accordingly  the  field  surrounding  a  straight  wire  may  be  looked 
upon  as  a  series  of  concentric  cylinders.  The  results  of  experi- 
ment 11  show  that  the  field  surrounding  a  current-bearing  wire 
affects  a  magnetic  needle,  and  that  it  is,  therefore,  magnetic. 
The  results  also  show  that  the  direction  of  the  deflection  of  the 
needle  is  determined  by  the  relative  position  of  wire,  needle  and 
the  direction  of  the  current  flow.  The  logical  conclusion  is, 

then,  that  the  magnetic  field 
around  an  electric  wire  has  di- 
rection, and  that  this  direction 
depends  upon  the  direction  of 
the  current  and  the  position  of 
the  wire.  Reversing  the  current 
~~j  N  flow  reverses  the  direction  of  the 

*  field. 

The  direction  of  the  field  can 
FIG.  23.  always    be    determined   by  the 

following  rule: 

Grasp  the  wire  with  the  right  hand,  the  thumb  pointing  in  the 
direction  of  the  current;  the  fingers  will  then  point  in  the  direction 
of  the  magnetic  lines  surrounding  the  wire. 

If  the  wire  is  near  a  magnetic  needle,  the  north  seeking  pole 
will  be  deflected  in  the  direction  indicated  by  the  fingers.  This 
rule  is  illustrated  by  Fig.  23. 

The  results  of  experiment  12  show  that  a  solenoid  has  the 
properties  of  a  bar  magnet,  the  two  ends  being  of  opposite 
polarity.  That  this  must  be  so  can  easily  be  determined  if  the 
student  will  carefully  consider  what  must  take  place  when  a 
current-bearing  wire  is  wound  into  a  circular  coil,  or  solenoid. 
Since  the  direction  of  the  magnetic  lines  is  determined  by  the 
direction  of  the  current,  when  the  wire  is  coiled,  the  lines  must 
enter  at  one  end  and  leave  at  the  other.  The  arrangement  of 
the  lines  within  a  solenoid  is  shown  in  Fig.  24.  It  will  be  noticed 
that  all  of  the  lines  do  not  go  the  full  length  of  the  coil,  but  many 
escape  between  the  convolutions  of  the  coil.  The  field  within 
the  solenoid  is  not  uniform  but  grows  weaker  from  the  center 
toward  the  ends.  The  end  from  which  the  lines  emerge  is  the 
north  seeking  pole,  while  the  other  end  is  the  south  seeking  pole. 


ELECTRON AGNETISM  27 

The  polarity  of  the  solenoid  can  readily  be  determined  by  the 
rule  for  determining  the  direction  of  the  magnetic  lines  about  a 
straight  conductor.  For  if  one  of  the  convolutions  or  turns  of 
wire  be  grasped  by  the  right  hand,  as  directed  in  the  rule,  the 
fingers  will  point  in  the  direction  of  the  north  seeking  pole  of 
the  solenoid.  The  same  relation  can,  however,  be  expressed  as 
follows :  //  an  observer  face  one  end  of  a  solenoid  and  the  current 
flows  in  a  counter-clockwise  direction,  the  north  seeking  pole  of 
the  solenoid  is  nearer  the  observer.  If  the  current  flows  in  a  clock- 
wise direction,  the  south  seeking  pole  is  nearer  the  observer. 

37.  Strength  of  Magnetic  Field  Around  an  Electric  Wire. — 
The  strength  of  a  magnetic  field  is  defined  in  terms  of  the  force 
it  exerts  upon  a  unit  magnet  pole.  Although  it  is  impossible 


FIG.  24. 

in  practice  to  develop  a  single  unit  pole,  nevertheless,  theoretic- 
ally a  unit  magnet  pole  is  defined  in  Article  10.  A  magnetic 
field  is  said  to  have  unit  strength  when  it  exerts  a  force  of  one 
dyne  upon  a  unit  magnet  pole.  Practically  it  is  impossible  to 
measure  the  strength  of  a  magnetic  field  in  this  way. 

Since  iron  filings  are  arranged  in  lines,  magnetic  fields  are 
always  described  as  though  they  consisted  of  lines,  and  a  unit 
magnetic  field  is  represented  as  consisting  of  one  line  per  square 
centimeter,  etc.  The  magnetic  field  due  to  an  electric  wire  is 
likewise  considered  as  though  it  were  made  up  of  lines  wrapped 
around  the  conductor.  The  strength  of  the  field  will  then  be 
represented  by  the  number  of  lines  per  square  centimeter  in  a 
plane  containing  the  wire.  The  density  or  number  of  lines  per 
square  centimeter  decreases  from  the  wire  outward.  Experi- 


28  MAGNETISM  AND  ELECTRICITY 

ments,  as  well  as  theory,  show  that  the  strength  of  a  magnetic 
field  at  any  point  due  to  a  current-bearing  wire  depends  directly 
upon  the  current  strength  and  inversely  upon  the  average  dis- 
tance of  the  point  from  the  wire.  In  algebraic  symbols  if  H 
represents  the  field  strength,  I  the  current,  and  d  the  distance 
of  a  point  from  the  wire,  then, 

27  _  twice  current 
~  d  ~      distance 

EXAMPLES 

1.  A  current  of  ten  units  flows  through  a  straight  wire.     What  is  the 
magnetic  field  strength  at  a  distance  of  5  cm.  from  the  wire? 

Solution.— 

I  =  10  units 
d  =  5  cm. 

Then  //  =  —  _  —  =  4  units 

o 

2.  A  field  of  5  units  exists  at  a  distance  of  5  cm.  from  a  given  current- 
bearing  wire.     What  is  the  field  strength  at  a  point  25  cm.  distant 
from  the  wire? 

Solution.  — 


Ht  =  is  unknown 
d2  =  25 

Then  5  =  ~ 

,   „      27 
and  #2=25 

jr  K 

Dividing  second  equation  by  first  we  get  ~F  =  05 

25 
Whence  HZ  =  ^  =  1  unit 

This  also  follows  from  the  relation  given,  increasing  the  distance  5 
times  decreases  the  field  strength  to  1/5;  hence,  1/5  of  5  =  1  unit. 

38.  Reaction  between  Electric  Wires.  —  When  two  current- 
bearing  wires  are  brought  near  each  other,  they  will  either  be 
attracted  or  repelled  if  parallel,  and  if  not  parallel  will  tend  to 
become  parallel.  The  force  of  attraction  or  repulsion  is  due  to 
the  interaction  of  the  two  magnetic  fields  around  the  wires.  The 
manner  in  which  such  a  force  develops  will  readily  be  understood 
from  Figs.  25  and  26.  If  the  two  wires  are  parallel  and  the  cur- 


ELECTROMAGNETISM  29 

rents  flow  in  the  same  direction,  the  magnetic  fields  will  combine 
and  encircle  both  wires  and  the  two  wires  will -be  drawn  toward 
each  other.  This  is  shown  by  Fig.  25. 

When  the  two  currents  flow  in  opposite  directions,  the  magnetic 
fields  cannot  combine  as  they  are  oppositely  directed.  The 
reaction  between  the  fields  will  tend  to  push  the  wires  farther 
apart.  These  conditions  are  represented  in  Fig.  26.  It  can  be 
shown  by  higher  mathematics  that  the  force  tending  to  draw  the 
wires  together,  or  to  push  them  apart  is  proportional  to  the  product 
of  the  currents  in  the  two  wires  so  long  as  the  wires  remain  in 
fixed  positions.  For  instance,  if  the  current  in  one  wire,  Fig.  25, 
is  10  units,  and  in  the  other  wire  the  current  is  5  units,  then  the 
force  pulling  one  toward  the  other  is  proportional  to  5X10. 
Its  exact  value  will  depend  upon  the  distance  between  the  two 


(.fiOk 


y 

•  Ii 


FIG.  25.  FIG.  26. 

wires.  This  principle  can  be  put  into  an  algebraic  equation,  as 
follows : 

Let  /i  =  current  in  one  wire. 

1 2  =  current  in  the  other  wire. 

Then  F  =  KXliXl2,  where  K  is  a  proportionality  factor  whose 
value  depends  upon  the  distance  between  the  wires.  When  the 
same  current  flows  in  the  two  wires,  Ii  =  Iz  =  I,  and  the  expres- 
sion for  the  force  becomes: 

F  =  KP,  which,  in  words,  means  that  the  force  is  proportional 
to  the  square  of  the  current.  This  principle  has  numerous 
practical  applications. 

If  two  conductors  are  mounted  in  such  a  way  that  the  force 
between  them  can  be  measured,  the  device  can  be  used  to  mea- 
sure the  current  flowing.  Several  electrical  measuring  instru- 
ments in  practical  use  operate  on  this  principle.  The  essential 
parts  of  the  simplest  instrument,  known  as  the  "  electrodyna- 
mometer  ammeter"  are  shown  in  Fig.  27,  and  an  actual  instru- 
ment is  shown  in  Fig.  28.  As  shown,  the  operating  part  of  the  in- 


30 


MAGNETISM  AND  ELECTRICITY 


strument  consists  of  two  coils,  FFf  and  MM'.  The  former  is  rig- 
idly attached  to  the  vertical  support  as  shown  in  Fig.  28,  and  the 
second  can  turn  around  a  vertical  axis.  The  current  to  be  meas- 
ured is  passed  into  coil  FF'  through  7\  and  after  passing  through 
FFf  it  enters  M  at  C  and  finally  leaves  the  movable  coil  at  T. 
The  student  will  observe  that  the  current  passes  upward  in  the 
side  F  of  the  fixed  coil  and  the  side  M  of  the  movable  coil.  Like- 
wise, it  passes  downward  in  F'  and  M'.  According  to  the  prin- 
ciple explained,  the  side  M  will  be  attracted  by  F  and  repelled 
by  F'j  and,  likewise,  the  side  M'  will  be  attracted  by  Ff  and  re- 


FIG.  28. 


pelled  by  F.  These  forces  of  attraction  and  repulsion  will  cause 
the  movable  coil  to  be  deflected.  By  turning  the  torsion  head 
G,  the  movable  coil  is.  brought  back  to  its  original  or  zero  posi- 
tion. The  angle  through  which  the  torsion  head  is  turned  is  a 
measure  of  the  force  tending  to  deflect  the  movable  coil.  Since, 
as  has  been  pointed  out,  this  force  is  proportional  to  the  square 
of  the  current  in  the  coils,  the  angle  through  which  the  torsion 
head  is  turned  to  bring  coil  MM'  to  its  zero  position  is  propor- 
tional to  the  square  of  the  current.  Hence,  if  we  know  what 
current  is  required  to  cause  unit  deflection,  we  can  calculate  the 
current.  The  movement  of  a  Weston  voltmeter  is  shown  in 


ELECTRON AGNETISM 


31 


Fig.  29.     The  student  will  readily  see  that  this  instrument  also 
operates  upon  the  same  principle. 

39.  Magnetic  Field  at  Center  of  a  Circular  Coil.— The  student 
has  already  learned  that  when  a  conductor  is  wound  into  the 

form  of  a  long  coil,  and  a  current 

is  passed  through  it,  the  solenoid 
has  the  properties  of  a  bar  mag- 
net. Much  the  same  principles 
hold  in  the  case  of  a  circular 
coil.  The  arrangement  of  iron 
filings  within  such  a  coil  is  shown 
in  Fig.  30.  The  end  of  the  coil 
where  the  lines  enter  has  the 
properties  of  a  magnetic  south 
pole,  and  the  other  end  those  of 
a  north  pole. 

We  have  already  suggested  a 
method  of  measuring  a  current 
by  the  interaction  of  the  mag- 
netic fields  surrounding  the  conductors.     In  order  to  measure 
a  current  by  its  magnetic  effect,  it  is  necessary  to  determine  some 
effect  which  shall  be  assumed  to  be  unity.     That  is,  the  effect 
selected  shall  represent  the  unit  used  in  measuring  the  current 


FIG.  29. 


FIG.  30. 


producing  it.  It  is  very  evident  that  in  selecting  such  a  unit 
the  effect  must  have  a  definite  relation  to  the  current.  The  sim- 
plest relation  is  where  the  effect  is  directly  proportional  to  the 
first  power  of  the  current.  Such  a  quantitative  relation  will  be 


32  MAGNETISM  AND  ELECTRICITY 

explained  later.     Now  we  are  concerned  with  the  magnetic  effect 
of  the  current. 

When  a  current  is  sent  through  a  circular  coil,  it  develops  a 
magnetic  field  at  the  center  of  the  coil.  The  strength  of  this 
field  is  also  directly  proportional  to  the  first  power  of  the  current, 
and  in  algebraic  symbols  we  can  express  this  relation  thus: 

H=  -  for  a  coil  of  one  turn,  where  /  is  the  current,  w  is  3.1416, 

r  the  radius  of  the  circle,  and  2w  is  2X3.1416.     The  mathematical 
derivation  of  this  formula  is  too  difficult  for  an  elementary  text. 

For  any  given  circular  coil  --  is  constant;  and,  accordingly,  we 

have  the  relation  mentioned,  namely,  that  the  strength  of  field  H 
is  directly  proportional  to  the  first  power  of  the  current. 

EXAMPLES 

1.  A  circular  coil  of  5  cm.  radius  carries  an  electric  current  of  5  electro- 
magnetic units.     What  is  the  field  strength  at  the  center  of  the  coil? 

Solution.  — 


7  =  5 
r  =  5 

2X3.1416X5 
Then  H  =  —    —  ^  —    —  =  6.28  gausses 

2.  What  is  the  current  which,  when  passed  through  a  circular  coil  of  2^ 
cm.  diameter,  develops  a  magnetic  field  of  2  gausses  at  the  center  of 
the  coil? 


Solution. — 


Solving  the  equation 
H  = for  7,  we  get 


r  =  10 

^  '=m° 

20 
=  ZToo=3.H-  units 


40.  Unit  of  Current. — The  above  relation  together  with  the 
definition  of  unit  magnet  pole  has  been  selected  as  the  basis  for 
defining  unit  current  and  is  as  follows:  A  unit  current  is  that 


ELECTROMAGNETISM  33 

current  which,  when  passing  through  an  arc  of  unit  length  in  a 
circle  of  unit  radius  will  produce  at  the  center  of  the  circle  a  mag- 
netic field  of  unit  intensity.  In  the  system  of  units  that  has  for 
its  fundamental  units  the  centimeter,  second,  and  gram,  the 
unit  arc  is  an  arc  of  1  cm.  the  unit  radius  is  1  cm.,  and  the  unit 
magnetic  field  is  one  that  exerts  a  force  of  1  dyne  upon  a  unit 
magnet  pole.  The  electromagnetic  unit  of  current  can  then  be 
defined  as  that  current  which,  when  flowing  through  a  conductor 
bent  into  a  circle  of  1  cm.  radius,  exerts  a  force  of  2?r  dynes  on 
a  unit  pole  at  the  center  of  the  circle  of  which  the  conductor 
is  the  circumference.  The  factor  2?r  is  used  because  the  circumfer- 
ence of  a  circle  is  2-jrr  =  2X3. 1416 Xr,  and  when  r=l  cm.,  this 
reduces  to  2ir  =  2  X  3. 1416.  If  the  current  exerts  a  force  of  1  dyne 
when  flowing  through  an  arc  1  cm.  long,  it  will  exert  a  force 
of  2-jT  dynes  when  passing  along  an  arc  2ir  cm.  long. 

This  unit  of  current  is  too  large  for  practical  purposes  and, 
therefore,  one-tenth  of  this  value  has  been  taken  as  the  practical 
unit  of  current,  and  is  called  an  ampere,  after  the  French  physi- 
cist, Ampere.  Later  we  shall  learn  how  a  current  may  be  meas- 
ured by  its  chemical  effect. 

The  first  practical  instrument  for  measuring  an  electrical 
current  was  operated  by  the  magnetic  effect  of  the  current.  The 
instrument  consisted  of  a  small  magnetic  needle  mounted  at  the 
center  of  a  circular  coil.  The  instrument  has  only  an  historical 
interest  at  present. 

41.  Electromagnets. — We  have  learned  that  a  solenoid  has 
the  properties  of  a  bar  magnet.     The  poles  of  a  solenoid  are  not, 
however,  very  strong  and  if  we  had  to  rely  upon  permanent 
magnets  and  solenoids  only  for  magnetic  fields,  none  of  the  large 
dynamo-electric  machines  would  be  possible.     It  is  the  combina- 
tion of  a  solenoid,  or  coil  of  other  form,  and  an  iron  core  that 
gives  the  strongest  magnetic  field.     This  principle  we  shall  now 
investigate. 

42.  Experiment  13.    Development  of  Magnetism  in  an  Iron 
Core  by  an  Electric  Current. 

Apparatus. — 
Solenoid 
Dry  cells 
Compass  needle 
1/2-in.  X  6-in.  bar  of  iron 
1/4-in.  X  12-in.  bar  of  iron 


34 


MAGNETISM  AND  ELECTRICITY 


Operation.  —  Connect  the  solenoid  and  two  dry  cells  in  series. 
Place  the  solenoid  and  compass  in  the  relative  position  shown  in 
Fig.  4.  The  solenoid  is  to  replace  the  bar  magnet  there  shown. 
Move  the  solenoid  either  nearer  to  or  farther  from  the  compass 
until  the  compass  needle  shows  a  deflection  of  only  one  or  two 
degrees.  Mark  on  the  table  the  position  of  the  solenoid.  Dis- 
connect the  solenoid  and  in  the  same  position  place  the  1/2-in.  X 
6-in.  iron  bar.  Again  observe  the  direction  and  amount  of  the 
deflection  of  the  compass  needle.  In  case  the  bar  has  been  pre- 
viously magnetized  and  the  compass  needle  is  deflected  in  a 

direction  opposite  to  that 
caused  by  the  solenoid  alone, 
turn  the  bar  end  for  end  and 
record  the  direction  and 
amount  of  the  deflection. 

Having  determined  the  in- 
fluence of  the  bar  and  solenoid 
singly,  connect  up  the  solenoid 
as  before  and  place  it  in  its 
previous  position.  Place  the 
bar  within  the  solenoid  and 
upon  closing  the  circuit,  deter- 

mine the  deflection  of  the  compass  needle.  Is  it  greater  than  the 
sum  of  the  deflections  caused  by  the  bar  and  solenoid  separately? 
Take  some  four-penny  nails  and  determine  how  many  will 
adhere  to  one  end  of  the  bar  when  the  solenoid  is  excited  by  one 
dry  cell.  Then  connect  successively  two  and  three  dry  cells 
in  series,  and  in  each  case  determine  the  number  of  nails  that 
can  be  suspended  from  one  end.  A  diagram  of  connections  is 
shown  in  Fig.  31.  Does  the  number  of  cells  in  series  have  any- 
thing to  do  with  the  strength  of  the  electromagnet? 

Place  the  electromagnet  in  a  horizontal  position  and  upon  it 
in  a  horizontal  position  place  a  stiff  sheet  of  paper.  Excite  the 
electromagnet  by  closing  the  key  and  sprinkle  iron  filings  upon 
the  sheet  of  paper.  Draw  a  diagram  showing  the  arrangement 
of  the  iron  filings.  Compare  this  diagram  with  the  magnetic 
field  of  a  bar  magnet. 
43.  Experiment  14.  Magnetic  Properties  of  U-shaped  Bar. 

Apparatus.  —  Same  as  in  experiment  13. 

Operation.  —  Bend  the  1/4-in.  piece  of  iron  into  the  shape  of 
the  letter  U  and  wind  each  prong  with  about  20  turns  of  insu- 


FIG< 


ELECTROMAGNETISM  35 

lated  wire.  The  current  must  flow  in  opposite  directions  around 
the  two  prongs.  Now  connect  two  dry  cells  to  the  two  free 
ends  of  the  wire  and  test  the  electromagnet  for  polarity.  Lay 
the  electromagnet  on  a  flat  surface  and  place  a  sheet  of  paper 
upon  it :  close  the  electric  circuit  and  sprinkle  iron  filings  over  the 
paper.  Draw  a  diagram  of  the  arrangement  of  the  iron  filings. 
Compare  your  diagram  with  the  diagram  of  the  magnetic  field 
of  a  horseshoe  magnet. 

Place  a  large  nail  across  the  poles  of  the  electromagnet.  Is 
the  nail  held  in  place  more  firmly  than  when  it  was  in  contact 
with  one  end  of  the  bar  electromagnet?  Hold  the  U-shaped 
electromagnet  in  an  inverted  position  and  break  the  electric 
circuit.  What  happens  to  the  nail? 

44.  Theory. — All  the  foregoing  principles  are  of  the  utmost 
importance  in  the  industrial  application  of  electricity.  It  was 
Joseph  Henry,  at  one  time  professor  of  physics  at  Princeton 
University,  who  discovered  the  effect  an  electric  current  has 
upon  a  soft-iron  bar. 

At  the  present  time  we  can  easily  make  the  simple  experiments 
which  show  the  electromagnetic  effect  of  the  current,  but  when 
Professor  Henry  made  his  experiments  no  insulated  wire  was 
available.  The  difficulty  of  the  task  is  at  once  apparent.  Fur- 
thermore, no  one  at  that  time  had  the  slightest  notion  as  to  how 
important  his  discoveries  were.  In  the  Library  of  Congress  at 
Washington  statues  are  arranged  around  the  reading  room  bal- 
cony, each  figure  symbolizing  important  advancement  in  some 
line.  A  statue  of  Joseph  Henry  with  a  small  electromagnet  in 
his  hand  is  used  to  symbolize  the  most  important  development 
in  electromagnetism. 

The  results  of  experiments  13  and  14  show  only  a  few  of  the 
effects  and  relations  between  an  electric  current  and  magnetism. 
Others  will  be  studied  later.  The  important  principles  devel- 
oped are  the  fact  that  a  current  passing  around  an  iron  bar  makes 
a  magnet  of  the  bar,  and  that  the  magnetic  strength  increases 
with  the  current  and  number  of  turns  of  wire  around  the  iron 
core. 

It  has  also  been  shown  that  the  electromagnet  is  much  stronger 
than  a  permanent  magnet  of  the  same  size.  The  electromagnet 
is,  however,  only  a  temporary  magnet,  as  the  experiments  show 
that  when  the  electric  circuit  was  broken  the  iron  core  lost  its 
magnetism. 


36  MAGNETISM  AND  ELECTRICITY 

45.  Magnetic  Field  Inside  of  a  Long  Solenoid. — Although  it 
is  somewhat  difficult  to  determine  the  mathematical  expression 
for  the  strength  of  the  magnetic  field  inside  of  a  long  solenoid, 
nevertheless,  the  expression  is  necessary  for  the  purpose  of  cal- 
culation.    It  can  be  shown  that  if  the  length  of  the  coil  is  not 
less  than  20  times  its  diameter,  the  field  at  the  center  of  the 
solenoid  is  practically  uniform,  and  that  its  value  is  given  by 

H  =  QATrnI  =  1.257  nl  gausses, 

where  n  is  the  number  of  turns  per  centimeter  length  of  coil, 
and  I  is  in  amperes. 

This  equation  also  holds  for  solenoids,  bent  so  as  to  form  a 
closed  ring.  The  magnetic  field  produced  by  a  ring  solenoid  is 
confined  entirely  to  the  closed  space  inside  the  spiral  forming 
the  ring. 

EXAMPLE 

A  solenoid  of  1,000  turns  is  20  cm.  long.  What  is  the  magnetic  field 
near  the  center  of  the  solenoid,  when  10  amperes  are  flowing  through  it? 

Solution. — 

H  =  1.257  nl 

1000      rrt 

n=  ~W  =5° 

/  =  10  amperes 
Then  #  =  1.257X50X10 
=  628 . 5  gausses 

46.  Permeability.— In  experiment  13  the  student  learned  that 
when  a  soft-iron  core  is  placed  within  a  solenoid,  the  resulting 
magnet  is  much  stronger  than  when  the  core  is  omitted.     The 
iron  possesses  the  property  of  increasing  the  magnetic  field 
strength.     The  magnetic  lines  are  concentrated  within  the  iron 
core  and  radiate  from  the  ends.     If  we  express  the  strength 
of  a  magnetic  field  within  the  solenoid  without  iron  by  H,  and 
if  B  represents  the  strength  of  the  magnetic  flux  within  the  iron 
core  when  it  is  subjected  to  the  magnetic  influence  of  the  solenoid, 
then  the  ratio  of  B  to  H  is  called  the  permeability.     This  ratio 
is  usually  expressed  by  the  Greek  letter  /-i  (mu).     Algebraically 
this  ratio  is  given  by 


ELECTROMAGNETISM 


37 


EXAMPLE 

A  certain  specimen  of  iron,  when  subjected  to  the  magnetic  influence  of 
a  solenoid  capable  of  creating  in  air  50  magnetic  lines  to  the  square  centi- 
meter, was  found  to  be  permeated  with  20,000  magnetic  lines  per  square 
centimeter.  What  is  the  permeability  of  the  iron? 


Solution. — 


B 


According  to  the  definition,  permeability,  /*= 


5=20,000 
#  =  50 


Hence,  /*== 


/5000 


/2000 


9000 


k 


£     6000 

I 

1 

&  3000 


sooo 


o  /  a 


e       e      /o 


FIG.  32. 


This  is  a  low  value,  for  a  good  iron  may  run  as  high  as  10,000. 
The  exact  value  of  the  permeability  depends  greatly  on  the 
quality  of  the  iron  and  its  previous  magnetic  history,  and  also 


38  MAGNETISM  AND  ELECTRICITY 

upon  the  degree  of  magnetization.  The  permeability  of  soft 
wrought  iron  is  greater  than  that  of  cast  iron;  and  that  for  mild 
or  open  hearth  steel,  as  now  made  for  electrical  machinery,  is  in 
some  cases  equal  to  that  of  the  best  soft  wrought  iron. 

The  results  of  the  two  previous  experiments  do  not  show 
clearly  the  dependence  of  the  magnetic  strength  upon  the  strength 
of  the  current,  because  the  experiments  are  only  illustrative. 
When,  however,  the  experiments  are  performed  in  such  a  way 
that  the  current  as  well  as  the  magnetic  flux  are  measured,  it  is 
found  that  when  the  current  is  very  weak  and  the  number  of 
turns  on  the  core  are  few,  the  magnetism  in  the  iron  core  is  low. 
When  the  current  strength  has  reached  a  certain  value,  the 
magnetic  flux  increases  greatly  for  a  small  increase  in  current. 
Beyond  this  point  the  magnetic  flux  increases  again  slowly. 
This  variation  in  flux  with  the  magnetizing  current  is  shown  in 
Fig.  32.  In  order  that  the  student  may  understand  the  curve, 
an  explanation  of  plotting  curves  will  be  given.  Curves  showing 
the  relation  between  the  variations  of  two  quantities  which  are 
mutually  dependent  are  of  extreme  importance  in  all  engineering 
work. 

47.  Curve  Plotting. — Where  the  value  of  one  quantity  depends 
upon,  or  varies  with  another  quantity,  the  character  of   the 
variation  is  most  clearly  shown  by  means  of  a  continuous  line 
or  curve  which  is  determined  in  accordance  with  the  following 
principles : 

First,  two  lines  or  axes  XX'  and  YY'  are  drawn  at  right  angles 
to  each  other,  Fig.  33.  These  two  axes  divide  the  plane  into  four 
parts  called  quadrants,  which  are  numbered  7,  //,  ///,  IV  in 
the  figure. 

A  point  is  located  on  a  plane  when  its  distances  from  the  axes 
are  known.  The  distance  of  the  point  from  the  axis  YY'  is 
called  its  z-distance,  or  abscissa;  its  distance  from  the  axis  XX' 
is  called  its  ^-distance,  or  ordinate.  The  two  distances  taken 
collectively  are  called  coordinates  of  the  point. 

48.  Signs  of  the  Coordinates. — For  purposes  of  uniformity 
mathematicians  have  agreed  that  distances  measured  to  the 
right  of  YY'  are  to  be  called  positive;  those  to  the  left  negative. 
Distances  measured  above  axis  XX'  are  positive;  those  below, 
negative.     Thus,  a  point  in  the  first,  quadrant  has  both  coordin- 
ates positive.     The  coordinates  of  a  point  in  the  third  quadrant 
are  both  negative.     The  second  quadrant,  the  abscissa,  is  nega- 


ELECTROMAGNETISM 


39 


tive  and  the  ordinate  positive,  while  in  the  fourth  quadrant  the 
abscissa  is  positive  and  the  ordinate  negative.  These  are 
shown  in  Fig.  33. 


II 

4 

Y 

, 

:. 

3 

(3.4) 

Z 

(-3,2) 

\ 

-3 

-2 

-1 

0 

i 

2 

3 

4 

C-3,-3) 

ft-3) 

1 

n 

Y' 

IV 

X 


FIG.  33. 


49.  Plotting. — The  locating  of  a  point  by  means  of  its  coordi- 
nates is  called  plotting  the  point.  To  locate  a  point  whose  coordi- 
nates are  (4,  5),  which  means  that  z  =  4,  y  =  5,  we  measure  from 
the  origin,  O,  to  the  right  on  OX  four  units,  and  then  from 
this  point  we  measure  up  5  units  parallel  to  OY.  The  point 
thus  reached  is  the  point  (4,  5).  Any  other  point  is  located 
in  the  same  manner. 

In  the  figure  are  shown  the  following  points  (3,  4),  (  —  3,  2), 
(-3,  -3),  (4,  -3). 

In  determining  a  line  or  curve  which  shows  the  variation  of 
one  quantity  with  reference  to  another,  we  first  locate  several 
points  and  through  these  draw  a  smooth  curve. 


40 


MAGNETISM  AND  ELECTRICITY 


»l€lm 


,  /ay 


38. 


(27.  SOJ- 


25.  47) 


40 


0         JO        2O       30        4O       SO       60 

Current  in  hundredths  of  an  ampere 

FIG.  34. 


ELECTRON AGNETISM  41 

EXAMPLE 

The  current  taken  by  a  110- volt  16-candle-power  lamp  at  different  vol- 
tages was  measured  with  the  following  results: 


Volts 

Amperes 

100  X  amperes 

47 

0.25 

25 

50 

0.27 

27 

65 

0.38 

38 

78 

0.47 

47 

97 

0.60 

60 

105 

0.65 

65 

To  determine  whether  the  current  increases  uniformly  with  the  voltage  we 
plot  a  curve  as  shown  in  Fig.  34.  Point  1  is  determined  by  counting  to  the 
right  25  units  (100  times  current),  and  up  47  units  (the  voltage  where  the 
current  is  0.25).  The  other  points  are  located  exactly  the  same  way.  The 
line  joining  points  1  and  6  is  practically  a  straight  line.  If  the  voltage  had 
been  reduced  to  zero,  that  is,  if  the  current  corresponding  to  voltages  less 
than  47  volts  had  been  determined,  the  curve  would  no  longer  be  a  straight 
line. 

50.  Magnetomotive  Force,  or  Magnetizing  Force,  of  a  Sole- 
noid.— The  magnetizing  effect  of  an  electrical  current  depends 
not  only  upon  the  current  strength,  but  also  upon  the  number 
of  turns  in  the  coil.  This  fact  can  easily  be 
shown  by  changing  the  number  of  turns  on 


a  solenoid,  while  the  current  is  maintained       t  *v"wr  \ 

constant.     A  current  of  10  amperes  flowing        "^  —  ......  —  —  '* 

through  a  coil  of  100  turns  has  the  same  mag-  '  FIG.  35. 
netizing  effect  as  a  current  of  5  amperes  in  200 
turns  or  1  ampere  in  1,000  turns.  The  exact  numerical  value 
of  the  magnetizing  force,  called  magnetomotive  force,  de- 
pends upon  the  units  used.  Since  a  unit  magnet  field  has  been 
defined  as  the  field  which  exerts  a  force  of  one  dyne  upon  a  unit 
magnet  pole,  the  magnetomotive  force  of  a  coil  is  measured  by 
the  work  expended  in  moving  a  unit  magnet  pole  around  the 
magnetic  circuit.  Thus  in  Fig.  35,  if  P  represents  a  unit  magnet 
pole,  the  magnetomotive  force  of  the  solenoid  will  be  measured 
by  the  work  expended  in  moving  P  around  the  dotted  line  against 
the  magnetizing  force.  It  can  readily  be  shown  that  the  mag- 
netomotive force  is  given  by 


where  T  =  3.1416 

N-  =  number  of  turns 
/  =  current  in  amperes 


42  MAGNETISM  AND  ELECTRICITY 

The  product  NI  is  called  ampere-turns,  and  0 ATT  =  1.257. 
Hence,  the  magnetomotive  force  is  equal  to 

M.M.F.  =  1.257  X  ampere  turns. 

The  unit  of  magnetomotive  force  is  called  a  gilbert  after  the 
physician  of  Queen  Elizabeth. 

EXAMPLE 

How  many  gilberts  will  a  current  of  15  amperes  develop  in  a  coil  of 
2,500  turns? 

Solution. — 

M.M.F.  =  1.257  NI. 
N  =  2,500 
7  =  15  amperes 
NI  =37,500 

M.M.F.  =  1.257X37,500 
=  40852. 5  gilberts 

With  these  explanations  in  mind  we  can  understand  the  manner 
in  which  the  curve,  Fig.  32,  is  plotted,  and  also  its  significance. 
A  coil  of  several  turns  is  wound  around  an  iron  ring.  In  series 
with  the  coil  and  a  source  of  current  is  connected  a  regulating 
rheostat  for  adjusting  the  current.  The  current  is  measured, 
and  then  according  to  the  above  example,  the  magnetizing  force 
is  calculated.  The  current  is  next  changed  and  again  measured. 
Every  time  the  current  is  measured  the  magnetic  flux  in  the 
iron  ring  is  determined.  The  number  of  magnetic  lines  per 
square  centimeter  are  then  plotted  vertically  while  the  corre- 
sponding magnetizing  force  causing  them  is  plotted  horizontally 
Through  the  points  thus  determined  a  smooth  curve  is  then 
drawn.  The  curve  shows  that  for  low  values  of  the  magneto- 
motive force  the  number  of  magnetic  lines  increases  slowly. 
Between  the  values  of  one  and  four  gilberts  the  increase  is 
quite  rapid,  and  above  that  value  the  ratio  of  magnetic  lines  to 
magnetomotive  force  decreases  rapidly.  The  permeability  of 
iron  is  evidently  not  constant.  If  the  permeability  were  con- 
stant, the  magnetization  curve  would  be  a  straight  line.  A 
knowledge  of  the  magnetic  properties  of  iron  is  of  very  great 
importance  in  the  design  of  electrical  machinery. 

61.  Magnetic  Hysteresis. — In  discussing  the  molecular  theory 
of  magnetism  it  was  pointed  out  that  when  a  bar  is  magnetized, 
all  or  nearly  all  of  the  molecules  have  been  lined  up  with  their 


ELEC  TROMAGNE  TISM 


43 


north  ends  pointing  in  one  direction  and  their  south  ends  point- 
ing in  the  other  direction.  A  diagram  to  illustrate  this  assump- 
tion is  shown  in  Fig.  13.  When  the  bar  is  magnetized  by  an 
electric  current,  or,  in  fact,  in  any  other  way,  some  energy  must 
be  spent  in  forcing  or  compelling  the  molecules  to  line  up.  In 


FIG.  36. 

magnetizing  by  direct  current,  this  energy  is  supplied  in  the 
first  fraction  of  a  second,  and  after  the  molecules  have  lined  up, 
or  the  bar  has  become  magnetized,  no  more  energy  is  spent  in 
overcoming  the  "frictional  resistance"  of  the  molecules.  If  all 
of  the  molecules  are  not  lined  up,  an  increase  in  the  current  will 
make  more  of  them  to  fall  in  line  and  this  will  go  on  until  all 


44       .         MAGNETISM  AND  ELECTRICITY 

have  been  turned  in  one  direction;  any  additional  current  has 
no  effect,  and  the  iron  is  said  to  be  saturated.  For  practical 
purposes  the  sample  of  iron  for  which  the  curve  is  shown  in  Fig. 
32  may  be  considered  saturated  at  any  point  above  the  sharp 
bend  or  knee.  That  is,  above  12,000  lines  per  square  centi- 
meter. If,  after  having  reached  a  certain  value,  the  magneto- 
motive force  is  gradually  decreased  and  if,  when  the  current 
reaches  zero,  it  is  reversed  and  increased  gradually  in  the  oppo- 
site direction  to  the  same  maximum  value  as  before,  the  magnet- 
ization curve  will  not  decrease  along  the  same  line  as  it  increased, 
but  will  remain  higher.  This  is  shown  in  Fig.  36.  When  the 
magnetizing  force  has  dropped  to  zero,  the  flux  density  is  still 
about  10,800  lines  per  square  centimeter.  This  value  is  called 
remanent  or  residual  magnetism.  The  flux  density  drops  to 
zero  only  after  the  magnetizing  force  has  been  reversed  and,  in 
the  illustration  shown,  reached  a  value  of  about  three  gilberts 
in  the  opposite  direction.  The  magnetizing  force  required  to 
reduce  the  residual  magnetism  to  zero  is  called  coercive  force. 
It  is  thus  evident  that  work  must  be  done  in  causing  the  mole- 
cules to  turn  around  and  point  in  the  opposite  direction.  The 
decreasing  values  of  the  flux  density  lag  behind  the  values  cor- 
responding to  the  increasing  values  of  the  flux  density.  This 
lagging  behind  has,  therefore,  been  given  the  name  hysteresis 
which  means  "  lagging  behind/'  and  the  area  bounded  by  the 
four  lines  A,  B,  C,  and  D  is  called  a  hysteresis  loop.  This  loop 
is  due  to  the  fact  that  some  work  must  be  done  in  magnetizing 
the  iron  first  in  one  direction  and  then  in  the  other  direction. 
The  wider  the  loop  the  greater  the  amount  of  energy  spent  in 
the  process  of  reversing  the  magnetization.  This  energy  ap- 
pears as  heat  in  the  iron,  and  is  lost  for  all  practical  purposes. 
For  electrical  machines  in  which  the  magnetization  is  variable, 
it  if-  of  great  importance  to  use  iron  whose  hysteresis  loop  is  very 
narrow  and  consequently  has  small  hysteresis  loss. 

RECAPITULATION 

1.  Electromagnetism  is  the  principle  of  developing  magnetism  by  means 
of  an  electric  current. 

2.  A  solenoid  is  a  helical  coil  of  wire  of  many  turns,  usually  of  circular 
cross-section.     The  field  intensity  within  a  long  solenoid  is  equal  to 
H  =  QAir  nl,  n=  number  of  turns  per  centimeter. 

3.  When  two  current-bearing  wires  are  parallel,  they  are  attracted 


ELECTRON  AGNETISM  45 

when  the  currents  flow  in  the  same  direction,  and  repelled  when 
the  currents  flow  in  opposite  directions. 

4.  To  determine  the  direction  of  the  magnetic  lines  around  a  current- 
bearing  wire,  grasp  the  wire  with  the  right  hand;  if  the  thumb 
points  in  the  direction  of  the  current  flow,  the  fingers  will  point 
in  the  direction  of  the  magnetic  lines  encircling  the  wire. 

5.  The  strength  of  a  magnetic  field  at  any  point  near  an  electric  wire 
increases  directly  as  the  current  and  inversely  as  the  distance  of 
the  point  from  the  wire;  thus: 


6.  The  reaction  between  the  two  coils  of  an  electrodynamometer  am- 
meter is  proportional  to  the  square  of  the  current;  thus: 

Deflection  =KI* 


[deflection 
Whence  /  =  *vr 


K 

7.  The  magnetic  field  at  the  center  of  a  circular  coil  is  also  propor- 
tional to  the  current  strength  and  inversely  as  the  radius;  thus: 


8.  The  absolute  electromagnetic  unit  of  current  is  that  current  which, 
when  flowing  in  a  conductor  bent  into  the  circumference  of  a 
circle  of  unit  radius,  exerts  a  force  of  2*-  dynes  upon  a  unit 
magnet  pole  at  the  center  of  the  circle.    This  unit  is  ten  times 
as  large  as  the  practical  unit  called  the  ampere. 

9.  An  electromagnet  is  a  solenoid  with  an  iron  core. 

10.  Permeability  is  the  property  of  iron  that  causes  it  both  to  concentrate 
and  to  increase  the  number  of  magnetic  lines  inside  of  a  coil  or 
solenoid  when  placed  within.     Numerically  it  is  the  ratio  of  the 
flux  density  to  the  field  strength  ;  thus, 

B 
"*H 

11.  The  magnetomotive  force  of  a  solenoid  is  proportional  to  the  product 
of  the  total  number  of  turns  by  the  current.    Numerically  it  is  given 
by 


—  1  .  257  ampere  turns 

The  unit  of  magnetomotive  force  is  the  gilbert;  or  the  ampere 
turn,  which  is  the  magnetomotive  force  produced  by  a  current 
of  one  ampere  in  one  turn  of  wire. 


46  MAGNETISM  AND  ELECTRICITY 

12.  Hysteresis  is  the  lagging  of  the  magnetic  flux  behind  the  magnet- 
izing field.    A  hysteresis  loop  is  the  area  bounded  by  curves  showing 
the  relation  between  the  magnetic  flux  and  the  magnetizing  field. 
Hysteresis  loss  is  the  energy  wasted  or  converted  into  heat  in  alter- 
nately magnetizing  iron.    The  area  of  the  loop  is  proportional  to 
the  loss. 

13.  Residual  or  remanent  magnetism  is  the  flux  that  remains  in  the  iron 
core  after  the  magnetizing  field  has  dropped  to  zero. 

14.  Coercive  force  is  the  value  of  the  magnetizing  field  which  is  required 
to  reduce  the  remanent  magnetism  to  zero. 


CHAPTER  III 
SOME  PRACTICAL  APPLICATIONS  OF  ELECTROMAGNETS 

In  the  preceding  chapter  it  was  shown  that  when  an  electric 
current  flows  around  an  iron  core,  the  iron  core  becomes  a  strong 
magnet.  In  this  chapter  we  shall  take  up  some  of  the  practical 
applications  of  this  principle. 

52.  Experiment  15.    To  Study  the  Construction  and  Opera- 
tion of  the  Electric  Bell. 
Apparatus. — 
Electric  bell 
Push-button  or  switch 
Connecting  wires 
Dry  cell 

Operation. — Connect  one  dry  cell,  bell,  and  switch  in  series  as 
indicated  in  Fig.  37.  In  this  diagram  the  standard  symbol  for  a 
cell  is  used.  The  short  line  represents  the  negative  or  zinc 
electrode,  and  the  long  line  the  positive  or  carbon  electrode. 

If  one  cell  will  not  cause  the  bell  to  ring  when  the  circuit  is 
closed,  connect  two  cells  in  series  in  the  circuit;  close  the  circuit 
and  observe  the  sparks  at  the  point  where  the  spring  to  which  the 
clapper  is  attached  touches  the  point  of  screw  P.  The  current 
crosses  at  this  point;  hence  the  circuit  is  broken  whenever  the 
spring  leaves  the  screw.  Trace  the  circuit  through  the  bell 
from  one  binding  post  to  the  other.  The  metal  frame  or  base  of 
the  bell  usually  forms  part  of  the  circuit.  Does  it  in  this  bell? 
There  are  four  posts  that  must  be  examined  carefully.  They  are 
the  two  binding  posts,  the  post  that  carries  the  screw  P  and  the 
upright  to  which  the  clapper  is  attached.  One  or  more  of  these 
will  be  found  to  be  electrically  insulated  from  the  base  by  means 
of  hard-rubber  or  fiber  washers.  Such  a  post  does  not  make 
electrical  contact  with  the  base,  and  the  electrical  current  cannot 
pass  between  them.  The  current  is  thus  compelled  to  follow  a 
definite  course  through  the  winding  and  base.  Draw  a  simplified 
diagram  showing  this  course  and  describe  it.  Mark  the  in- 
sulated posts  in  this  diagram,  and  represent  by  a  dotted  line  the 
path  of  the  circuit  formed  by  the  metal  base  of  the  bell. 
6  47 


48 


MAGNETISM  AND  ELECTRICITY 


Examine  the  winding  on  the  electromagnet  and  determine  if 
the  two  parts  are  wound  in  the  same  direction.  What  is  the 
purpose  of  the  iron  core?  Why  is  there  an  iron  yoke  across  the 
ends  of  the  cores  at  A?  Is  the  enlargement  of  the  clapper  stem, 
S,  of  soft  iron,  brass,  or  hard  steel?  How  can  you  tell?  This 
part  of  the  stem  is  called  the  armature.  Why  does  not  the 
armature  remain  in  contact  with  the  iron  cores  when  drawn  up? 
Are  the  two  exposed  ends  of  the  electromagnet  core  of  like  or 
unlike  polarity?  How  can  you  tell?  Explain  the  action  of  the 

bell.  How  would  the  bell  be- 
have if  the  circuit  were  such  as 
to  send  the  current  through  the 
electromagnet  without  crossing 
between  the  screw  and  spring? 
Try  this  by  connecting  a  piece 
of  wire  between  P  and  S  so  that 
it  remains  in  contact  with  P  and 
S  all  the  time.  Does  the  bell 
continue  to  ring? 

If  you  have  two  electric  bells 
connect  them  in  series;  that  is, 
connect  a  binding  post  of  one  bell 
to  a  binding  post  of  the  other  bell 
and  connect  the  battery  to  the 
two  free  binding  posts,  one  on 
each  bell.  Close  the  circuit;  do 
the  bells  ring?  Do  they  ring 

as  when  used  singly?  If  you  think  the  trouble  is  due  to  weak 
current,  put  more  batteries  in  the  circuit.  Explain.  Connect 
the  two  bells  in  parallel;  that  is,  take  two  wires  and  connect  the 
two  binding  posts  of  the  bell  in  circuit  to  the  two  binding  posts 
of  the  second  bell.  Close  the  switch  and  note  results.  Do  the 
bells  ring  better  than  when  connected  in  series?  Explain. 

53.  The  Telegraph. — The  fundamental  principles  of  the  opera- 
tion of  the  telegraph  are  almost  exactly  the  same  as  those  of  the 
electric  bell.  To  make  this  clear  the  student  should  perform 
the  following  experiment. 

64.  Experiment  16.    To  Study  the  Principles  of  the  Telegraph. 
Apparatus. — Same  as  in  preceding  experiment. 
Operation. — Connect  the  apparatus  as  in  Fig.  37.     Connect 
the  binding  posts  C  and  P  together  by  means  of  a  piece  of  wire. 


FIG.  37. 


APPLICATIONS  OF  ELECTROMAGNETS 


49 


Close  the  electrical  circuit  by  touching  together  the  ends  of  the 
wire  and  observe  the  behavior  of  the  clapper.  Make  and  break 
the  circuit  rapidly.  What  is  the  result?  Can  such  a  device 
be  used  to  signal  at  some  distance? 

55.  Theory. — It  is  evident  that  when  the  circuit  is  closed  at 
short  intervals  these  short  intervals  may  be  represented  by  dots 
and  the  long  intervals  may  be  represented  by  dashes.  Thus 
three  short,  or  rapid  strokes  followed  by  three  long  and  three 

short  strokes  may  be  represented   thus    •  •  • •  •  •   which 

is  the  international  wireless  telegraph  distress  signal.  In 
practice  many  modifications  of  the  simple  apparatus  must  be 
made  in  order  that  the  signals  may  be  transmitted  easily  and 
rapidly,  and  for  long-distance  transmission.  It  must  be  evident 
that  if  two  such  bells  are  connected  to  the  same  circuit  some 


K 


FIG.  38. 


FIG.  39. 


distance  apart  and  each  is  provided  with  a  make  and  break  key, 
signals  can  be  transmitted  between  the  two  stations.  For 
instance,  if  one  key  is  kept  closed,  making  and  breaking  the 
circuit  at  the  other  station  will  operate  the  bell  at  the  distant 
station.  To  facilitate  the  making  and  breaking  of  the  electrical 
circuit  a  special  key  must  be  used.  This  key  is  shown  in  Fig.  38. 
The  key  is  so  constructed  that  every  time  the  lever  K  is  pressed 
down  a  current  is  sent  over  the  wire.  When  the  key  is  not  in 
use  in  forwarding  messages,  the  switch  S  short  circuits  the  lever 
K  so  that  messages  can  be  received.  At  each  end  of  the  line,  the 
bell  is  replaced  by  a  properly  mounted  electromagnet  called  a 
sounder.  This  operates  on  exactly  the  same  principle  as  the 
bell  with  the  wire  connection  between  posts  C  and  P.  In  place 
of  the  bell  the  sounder  is  mounted  on  a  resonant  base,  and  the 
stop,  which  corresponds  to  the  clapper  in  the  bell,  strikes  a  metal 
anvil,  t,  Fig.  39,  giving  forth  a  metallic  click. 

It  is  not  practical  to  send  signals  over  long  distances    with 


50 


MAGNETISM  AND  ELECTRICITY 


the  simple  circuit  described,  on  account  of  the  small  current. 
To  overcome  this  defect,  the  line  current  is  used  merely  to  open 
and  close  a  secondary  circuit  which  consists  of  a  battery  and 
sounder.  The  opening  and  closing  of  the  secondary  circuit  is 
accomplished  by  means  of  another  form  of  electromagnet  called 
a  relay.  Such  an  instrument  is  shown  in  Fig.  40.  The  electro- 
magnet of  the  relay  is  magnetized  by  the  line  current  while  the 


ARMATURE   CONTACT  POINTS 


ELECTRO  MAGNET 


SPRINGS 

AOJUSTIKQ  SCREW 


FIG.  40. 

armature  of  the  electromagnet  acts  as  a  key  in  the  local  battery 
circuit,  closing  and  opening  the  circuit  every  time  the  main  cir- 
cuit is  closed  or  opened.  The  manner  in  which  this  is  done  will 
be  understood  readily  from  Fig.  41.  In  this  diagram  a  and  a' 
are  the  two  line  wires  connected  to  the  electromagnet  of  the 
relay.  As  the  electromagnet  is  energized  the  armature  is  at- 


UOCAL.    8ATTEWV 

FIG.  41. 

tracted,  closing  the  local  battery  circuit  at  6.  The  sounder  is 
then  operated  by  the  current  from  the  local  battery  and  the 
click  may  be  made  as  loud  as  desired. 

Fig.  42  is  a  diagram  showing  how  the  principles  just  explained 
are  carried  out  in  practice.  At  each  station  is  a  circuit  consist- 
ing of  a  local  battery,  the  sounder  electromagnet,  and  the  arma- 
ture of  the  relay  the  electromagnet  of  which  is  in  the  line  circuit. 


APPLICATIONS  OF  ELECTROMAGNETS 


51 


The  ground  is  used  as  one  side  of  the  line.  If  La  Crosse  wishes 
to  call  Milwaukee,  the  switch  S  at  La  Crosse  is  opened  as  indi- 
cated. By  closing  and  opening  the  key  at  La  Crosse  the  relays 
at  both  Madison  and  Milwaukee  will  operate,  but  since  each 
station  has  its  own  signal,  Milwaukee  alone  will  answer.  The 
armature  P  of  the  Milwaukee  relay  operates  in  unison  with  the 
key  at  La  Crosse,  and  as  a  consequence  the  local  circuit  at  Mil- 
waukee is  opened  and  closed  and  the  sounder  clicks  at  the  will 
of  the  La  Crosse  operator. 


MILWAUKEE 


LACROSSE 


FIG.  42. 

56.  The  Telephone. — The  principles  of  electromagnetism  are 
also  used  in  the  transmission  of  speech  by  telephone  as  well  as 
by  telegraph.     The  operation  of  the  telegraph  depends  almost 
wholly  upon  the  magnetizing  property  of  an  electric  current  while 
several  other  principles  enter  into  the  operation  of  the  telephone. 
Only  the  application  of  the  principles  of  electromagnetism  will 
be  pointed  out  and  explained. 

57.  Experiment  17.    To  Study  the  Principles  of  Telephone 
Receivers. 

Apparatus. — 

Telephone  receiver 
Iron  filings 
Dry  cell 
Operation. — Unscrew  the  cap  from  the  large  end  of  the  tele- 


52 


MAGNETISM  AND  ELECTRICITY 


o 

•a 


APPLICATIONS  OF  ELECTROMAGNETS  53 


PLATE  3. — Terminal  room,  Wis.  Telephone  Co.,  Baraboo,  Wis. 


54 


MAGNETISM  AND  ELECTRICITY 


T' 


phone  receiver.  Under  this  cap  you  will  find  an  enameled  iron 
disk  resting  on  a  metal  ring.  Remove  this  disk.  Why  does  it 
stick  in  place?  Touch  the  ends  of  the  pole  pieces  with  the  edge 
of  the  disk.  What  do  you  discover?  Take  hold  of  the  iron  ring 
and  withdraw  the  magnet  from  the  casing.  This  receiver  is 
purposely  constructed  so  that  it  can  be  taken  apart  easily. 
Take  the  bar  magnet  and  determine  which  parts  are  magnetic 
and  which  are  non-magnetic.  Examine  the  winding  about  the 
pole  pieces.  Draw  a  sketch  of  the  magnetic  and  electric  circuit. 

Replace  the  magnet  within  the  re- 
ceiver and  hold  it  vertically  with  the 
large  end  up.  Place  a  piece  .of  card- 
board or  stiff  paper  over  the  pole  pieces 
and  sprinkle  some  iron  filings  on  top 
of  this.  Gently  tap  the  paper  and 
observe  the  arrangement  of  the  iron 
filings.  Are  the  pole  pieces  like  or  un- 
like? Sketch  the  resulting  magnetic 
field.  Replace  the  diaphragm  and 
cap.  Connect  one  end  of  the  receiver 
cord  to  one  binding  post  of  a  dry  cell, 
and  while  holding  the  receiver  near 
the  ear,  touch  the  other  binding  post 
of  the  dry  cell  with  the  other  end 
of  the  cord.  What  causes  the  click 
in  the  receiver?  Make  and  break  the 
circuit  rapidly;  what  do  you  hear? 

58.  Theory. — The  preceding  experi- 
ment shows  only  that  the  essential 
principles  of  a  telephone  receiver  are 

the  superposition  of  an  electromagnetic  field  upon  a  permanent 
magnet  field.  Fig.  43  shows  the  essential  features  of  a  very 
common  bi-polar  receiver.  The  shell  is  of  hard  rubber  and  is  in 
three  parts.  Two  permanent  bar  magnets  are  employed,  the  two 
being  fastened  together  at  one  end  and  thus  forming  practically 
one  magnet  of  the  horseshoe  form.  To  the  other  ends  of  the 
bar  magnets  are  fastened  two  soft-iron  pole  pieces  P  and  P'. 
Each  of  these  pole  pieces  is  wound  with  a  coil  of  fine  insulated 
copper  wire,  marked  M  and  M'  in  the  figure.  Immediately  in 
front  of  the  pole  pieces  is  fixed  a  sheet-iron  diaphragm,  D.  The 
diaphragm  forms  a  part  of  the  magnetic  circuit;  where  the  mag- 


FIG.  43. 


APPLICATIONS  OF  ELECTROMAGNETS  55 

netic  lines  enter  the  diaphragm  a  south  pole  is  induced,  and  where 
they  leave  a  north  pole  is  formed.  Thus  the  diaphragm  acts  as 
an  armature  and  is  bent  or  dished  toward  the  pole  pieces. 

The  coils  on  the  pole  pieces  are  wound  in  opposite  directions, 
so  that  when  a  current  flows  in  them  in  one  direction  they 
strengthen  the  field  of  the  permanent  magnet,  and  when  a 
current  flows  in  the  opposite  direction,  the  permanent  magnet 
field  is  weakened.  This  strengthening  and  weakening  of  the 
magnetic  field  causes  the  diaphragm  to  vibrate.  When  the 
field  is  strengthened,  the  "diaphragm  is  drawn  nearer  to  the  pole 
pieces,  and  when  the  current  ceases  the  diaphragm  springs  back 
to  its  normal  position.  When  the  current  in  the  coils  opposes 
the  permanent  magnetic  field,  the  diaphragm  springs  still  farther 
away  from  the  pole  pieces  and  when  the  current  ceases  it  again 
resumes  its  position  as  determined  by  the  attraction  of  the 
permanent  field.  It  is  thus  evident,  that  if  the  current  flows 
in  the  coils  first  in  one  direction  and  then  in  the  other,  or  if  an 
alternating  current  flows  in  the  receiver  coils,  the  diaphragm  will 
respond  to  every  impulse  of  the  current,  no  matter  from  which 
direction  it  comes. 

If  the  receiver  were  not  equipped  with  a  permanent  magnet, 
a  magnetic  field  would  be  formed,  no  matter  in  which  direction 
the  current  flowed.  The  diaphragm  would  be  attracted  or  drawn 
in  toward  the  pole  pieces  in  either  case,  and  would  spring  back 
to  its  neutral  position  when  the  current  ceased  to  flow.  The 
diaphragm  would  thus  vibrate  twice  as  rapidly  as  when  a  per- 
manent magnet  is  used. 

Then,  again,  the  successive  strengthening  and  weakening  of 
the  permanent  magnet  field  permits  or  causes  the  diaphragm  to 
vibrate  through  a  greater  space  than  would  be  the  case  if  a  soft 
iron  core  were  used. 

In  a  complete  telephone  circuit  there  are  other  electromagnets, 
but  these  will  not  be  explained  at  this  time. 

59.  Lifting  Magnets. — The  usual  method  of  hoisting  or  lifting 
heavy,  irregular  shaped  pieces  of  iron  is  rather  inconvenient 
sometimes.  For  instance,  large  bundles  of  sheet  iron,  or  bars 
of  pig  iron,  are  extremely  difficult  to  lift  by  means  of  a  hook  and 
chain.  The  lifting  magnet  overcomes  this  difficulty.  Fig.  44 
shows  a  large  lifting  magnet  hoisting  some  pig  iron.  The  manner 
in  which  such  a  magnet  is  excited  or  magnetized  will  be  under- 
stood readily  from  Fig.  45,  which  shows  a  cross-section  of  a 


56 


MAGNETISM  AND  ELECTRICITY 


FIG.  44. 


APPLICATIONS  OF  ELECTROMAGNETS 


57 


Cutler-Hammer  lifting  magnet.  The  essential  feature  of  the 
magnet  is  a  hollow  steel  casing  around  the  central  portion  of 
which  is  wound  a  coil,  C,  of  strap  copper  insulated  with  mica 
and  asbestos.  The  two  ends  of  the  coil  are  brought  out  through 
a  piece  of  armored  hose  at  A  and  B.  Direct  current  only  is 
used  for  excitation.  The  current  flowing  through  the  coil 
magnetizes  the  steel  casing  in  such  a  manner  that  the  central 
portion  is  of  one  polarity  and  the  outer  rim  of  the  opposite 
polarity.  The  cross-section  can  thus  be  represented  by  two  horse- 
shoe magnets  with  the  two  like  poles  placed  together  within  a 
circular  coil,  while  the  other  two  poles  are  outside.  The  piece  of 
iron  that  is  lifted  acts  as  the  armature  or  keeper.  The  traction 
or  lifting  power  of  such  magnets  is  very  high  when  the  size  of  the 
magnet  is  considered. 


FIG.  45. 

Lifting  magnets  are  made  of  different  shapes  according  to  the 
purpose  for  which  they  are  intended.  Where  large  sheets,  such 
as  boiler  iron  or  sheet  iron,  are  to  be  lifted,  the  electromagnets  are 
made  with  several  short  projecting  poles  each  wound  with  a 
magnetizing  coil.  For  carrying  scrap  iron  or  pig  iron  of  irregular 
form,  electromagnets  are  made  with  long  projecting  poles,  which 
may  be  sunk  into  a  heap  of  the  iron.  The  pieces  will  stick  to  the 
poles  on  all  sides. 

60.  Lifting  Force  of  Electromagnets. — The  lifting  power  of  an 
electromagnet  depends  not  only  upon  its  construction  and  on  the 
exciting  current,  but  also  upon  the  form  of  the  piece  to  be  lifted, 
and  upon  the  quality  of  the  iron  in  it.  This  is  because  the 
magnetic  flux  is  closed  through  the  piece  to  be  lifted;  hence  the 
properties  of  the  piece  to  be  lifted  determine  the  flux  values. 


58  MAGNETISM  AND  ELECTRICITY 

Assuming  that  the  piece  to  be  lifted  is  made  of  the  same  material 
as  the  core  of  the  lifting  magnet,  and  that  its  cross-section  is  equal 
to  that  of  the  magnet  core,  the  general  principles  of  electro- 
magnet design  can  be  given  readily.  It  can  be  shown  by  ex- 
periment and  by  higher  mathematics  that  the  force  of  attraction 
between  two  magnetized  pieces  of  iron  is  proportional  to  the 
square  of  the  flux  density;  that  is,  to  the  square  of  the  number 
of  magnetic  lines  per  square  centimeter.  Thus,  if  in  Fig.  46  the 
flux  density  be  represented  by  B,  the  force  tending  to  draw  the 
two  pole  pieces  together  is  proportional  to  B2.  If  the  cross- 


FIG.  46. 

sectional  area  of  the  magnetic  field  in  a  plane  perpendicular  to 
the  paper  is  S  square  centimeters,  the  force  tending  to  draw  the 
two  poles  together  is  proportional  to  the  area  S  times  the  square 
of  the  flux  density,  or,  in  algebraic  symbols, 

SB* 
Force  =-g^ 

This,  of  course,  is  on  the  assumption  that  the  flux  density,  B, 
is  uniformly  distributed  over  the  pole  faces. 

EXAMPLE 

How  many  dynes  of  force  will  an  electromagnet  exert  if  its  area  of  con- 
tact is  20  sq.  cm.  (3.1  sq.  in.),  and  if  it  is  magnetized  to  a  flux  density  of 
7,000  lines  per  square  centimeter? 

Solution.  —  According  to  the  formula  the  force  is  given  by 
„     AreaX#2 

"    STT 

area  =  20  sq.  cm. 
5  =  7,000 
TT  =3.1416 

20X7000X7000 
Then  F  (dynes)  = 


=  38,993,000  dynes  (nearly)  =87.6  Ib. 

In  this  country  the  English  system  of  units  is  more  commonly 
used  in  practice,  and  accordingly  it  is  advisable  to  transform  the 
above  formula  to  these  units.  In  practice  the  area  of  con- 


APPLICATIONS  OF  ELECTROMAGNETS 


59 


tact,  S,  is  usually  given  in  square  inches  and  the  flux  density  B 
is  given  in  lines  per  square  inch.  The  manner  of  transforming 
the  equation  in  which  metric  units  are  used  into  one  in  which 
the  English  units  are  used  will  be  understood  readily  by  refer- 
ence to  Fig.  47,  which  represents  a  surface  of  1  sq.  in.  at  right 
angles  to  a  magnetic  field.  The  dots 
are  assumed  to  represent  the  magnetic 
lines.  To  change  an  area  that  is  ex- 
pressed in  square  inches  to  square  cen- 
timeters it  is  only  necessary  to  multiply 
the  number  of  square  inches  by  6.452  as 
there  are  6.452  sq.  cm.  in  1  sq.  in. 

If  the  flux  density  is  expressed  in 
lines  per  square  inch,  the  number  of  lines 
per  square  centimeter  is-  obtained  by  di-  FIG.  47. 

viding  by  6.452.     Thus  if  the  area  is  S 

jsquare  inches,  and  the  flux  density  is  B  lines  per  square  inch, 
'the  expression  for  force  in  dynes  becomes 


6.452SX 


F  = 


6.452 


dynes 


Sir 

To  change  this  to  pounds  divide  by  444,793=445,000  nearly. 
We  then  get 


6.452SX 


F(pounds)  = 


B 


Y 


6.4527 


444793  X&r 

6.452XSX52 


Force  = 


6.452X6.452X444793X8X7T 
_iS(sq.  in.)  B2  (per  sq.  in.) 

6.452X444793X8XT 
£(sq.  in.)X#2(Per  sq.  in.) 
72126000 


The  student  must  remember  that  in  the  above  equation  S  is 
in  square  inches,  and  B  is  the  flux  density  per  square  inch. 


EXAMPLE 

What  weight  will  an  electromagnet  lift  whose  area  of  contact  is  1.66  sq. 
in.,  and  flux  density  is  83,850  lines  per  square  inch? 


60  MAGNETISM  AND  ELECTRICITY 

Solution. — 

SB1 


72126000 
S  =  1 . 66  sq.  in. 
5=83,850 

,  x     1  66X83850X83850 
F(pounds)  =          7212600o 

=  161.8  Ib. 

The  student  will  readily  see  that  this  is  a  small  magnet,  as  the  area  of 
contact  is  only  1 . 66  sq.  in. 

61.  Traction  and  Magnetizing  Force. — Summarizing  some  of 
the  principles  of  the  magnetic  circuit  so  far  discussed  we  have: 
S  —  Cross-sectional  area 
1= Length  of  magnetic  circuit  in  centimeters 
H  =  Magnetic  field  within  solenoid  without  iron 
B  =  Flux  density  or  number  of  lines  per  unit  area  within 
iron  core  placed  in  the  solenoid 

D 

M  =  permeability  =  ^ 

Magnetizing  force  of  solenoid  M.M.F.  =  1.257  NI.  Assuming 
that  there  is  no  magnetic  leakage  we  can  calculate  the  relation 
between  lifting  force  and  these  quantities  as  follows: 

The  magnetic  field  of  a  solenoid  has  been  shown  to  be  H 
=  1.257  nl  where  n  is  the  number  of  turns  per  centimeter 
length  of  the  solenoid.  In  the  above  expression  for  magnetizing 

N  1  257  NI 

force  N  is  the  total  number  of  turns.     Then  n  =  -y-  and  H=—  —7 — 

i  l> 

That  is,  the  field  within  a  solenoid  of  N  turns  through  which  a 
current  of  7  amperes  is  flowing  is  equal  to  1. 257  X  ampere  turns 
per  unit  length  of  magnetic  circuit.  From  the  relation,  flux 
density  =  permeability  X  field  strength,  B  =  jj,H,  we  get 

1. 


Putting  this  value  of  B  for  B  in  the  expression  for  the  lifting  force 
of  the  electromagnet  we  get 

(1.257  JV7M)2 
S(sq.cm.)-    p(em0 

F(dynes)=-  -- 


When  S  is  in  square  inches,  it  must  be  multiplied  by  6.452  to 
change  it  to  square  centimeters.     Likewise,  if  I  is  in  inches  it 


APPLICATIONS  OF  ELECTROMAGNETS  61 

must  be  multiplied  by  2.54  to  change  it  to  centimeters.  But  I  is 
squared,  and  squaring  2.54  we  get  6.452.  The  expression  then 
becomes 

6 
o. 

F  =  — 


STT 
SX  (1.257 


Swl* 

To  change  this  to  pounds  we  must  divide  by  444,793   (nearly 
445,000)  and  we  thus  finally  get 

_,          ,  , 
^(pounds)  « 

~ 


7075000  XI2 

EXAMPLES 

The  lifting  magnet,  the  contact  area  of  which  was  given  as  1.66  sq.  in., 
is  wound  with  90  turns  of  wire,  and  the  mean  magnetic  path  is  5  .  12  in.  How 
much  can  the  magnet  lift  if  it  is  magnetized  by  a  current  of  1.00  ampere 
and  its  permeability  is  1610? 

Solution.  — 

£  =  1.66  sq.  in. 
AT  =90  turns 
7  =  1.00  ampere 


Z  =  5.12in. 

1.66X90X90X1X1X1610X1610 
Then  t  =  7075000X5.12X5.12 

=  188.01b. 

Since  the  permeability  of  a  piece  of  iron  is  a  variable  quantity, 
the  relation  between  lifting  power  and  magnetizing  current  is 
not  a  straight  line  relation.  This  is  seen  readily  from  Fig.  48, 
the  data  for  which  were  obtained  by  testing  the  small  magnet 
already  mentioned,  and  are  given  in  the  following  table : 

TABLE  I 


Current              |             Weight  lifted 

0.25 
0.50 
0.75 
1.00 

33.75 
79.50 
134.25 
164.25 

62 


MAGNETISM  AND  ELECTRICITY 


To  facilitate  computation  a  table  is  added  which  shows  the 
relation  between  flux  density  and  lifting  force.  The  flux  density 
is  given  in  lines  per  square  inch,  and  lifting  force  in  pounds  per 
square  inch. 


KM) 

ISO 
160 

* 

fl.    |4p 

z  • 

-    ltd 

UJ 

0    80 

j 

40 

20 

/ 

s 

/ 

/* 

/ 

/ 

/* 

x 

/ 

0       .i     .2,    .3     A    .5    .6     rr     a     .9     1.0    i. 

CURRENT    JN  AMPERES 

FIG.  48. 
TABLE  II 


Lines  per  sq.  in. 


Pounds  per  sq.  in. 


6,450 

0.577 

12,900 

2.308 

19,350 

5.190 

25,800 

9.228 

32,250 

14.39 

38,700 

20.75 

45,150 

28.26 

51,600 

36.95 

58,050 

46.72 

64,500 

57.68 

70,950 

69.77 

77,400 

83.07 

83,850 

97.47 

90,300 

113.1 

96,750 

129.7 

103,200 

147.7 

109,650 

166.6 

116,100 

186.8 

122,550 

208.1 

129,000 

230.8 

APPLICATIONS  OF  ELECTROMAGNETS 


63 


The  practical  applications  of  electromagnets  are  too  numerous 
to  permit  of  listing  them.  A  most  important  use  is  the  magnetic 
field  of  all  dynamoelectric  machinery,  one  form  of  which  is  shown 
in  Fig  49.  This  shows  the  electromagnets  which  develop  the 
magnetic  field  of  the  direct-current  generator. 

Circuit   breakers,   the   clutches  of  arc  lamps,  motor  control 


FIG.  40. 

apparatus,  the  magnetic  brake,  magnetic  ore  separators,  etc.,  are 
all  operated  by  electromagnets. 

RECAPITULATION 

1  .  The  pull  of  an  electromagnet  is  given  by 

SB* 


where  S  =  area  of  contact  in  square  centimeters 

B  =  flux  density  in  lines  per  square  centimeter 

2.  When  the  area  of  contact  is  given  in  square  inches,  and  the  flux, 
density  in  lines  per  square  inch,  the  pull  in  pounds  is 

S  (sq.  in.)X#  (per  sq.  in.)  Ib. 
72126000 


64  MAGNETISM  AND  ELECTRICITY 

3.  When  an  electromagnet  is  excited  by  a  current  of  /  amperes  flowing 
through  N  turns  on  an  iron  core  of  permeability  n  and  length  of 
magnetic  path  I,  the  pull  is 

£(sq.in.) 


7075000  lz 


CHAPTER  IV 
ELECTROMAGNETIC  INDUCTION 

62.  Introduction. — In   the  preceding   chapters   we   discussed 
the  magnetism  produced  by  an  electric  current  when  flowing 
through  a  coil  of  insulated  wire.     Some  important  applications 
of  this  principle  were  also  briefly  pointed  out.     If,  however, 
magnetism  could  be  produced  only  by  a  current  from  a  battery, 
the  industrial  applications  of  electricity  would  be  very  limited. 
We  could  still  use  electricity  for  the  operation  of  electric  bells, 
the  telegraph,  telephones  for  short  distances,  and  perhaps  a  few 
other    minor    uses.     Electric    lighting,    electric   railways,    and 
allied  applications  would  be  practically  unknown  except  as  toys. 
It  is  the  generation  or  development  of  electric  current  by  means 
of  the  dynamo  that  has  made  possible  the  extended  use  of  elec- 
tricity in  the  distribution  of  power,  production  of  light,  electro- 
lysis, transmission  of  intelligence,  heating,  etc. 

Electromagnetic  induction  is  the  principle  that  whenever  the 
number  of  magnetic  lines  linking  a  circuit  is  changed,  an  elec- 
trical pressure  is  developed  within  the  conductor  forming  the 
circuit.  The  fundamental  principles  underlying  the  electro- 
magnetic development  of  the  electrical  current  will  now  be  taken 
up. 

63.  Experiment  18.    To  Study  Electromagnetic  Induction. 
Apparatus. — 

Galvanoscope 
Bar  magnets 
Horseshoe  magnet 
Solenoid 
Dry  cell 
Wires 

Operation. — This  experiment  is  perhaps  the  most  important 
that  the  student  has  been  asked  to  perform  so  far,  and  it  should 
therefore  be  repeated  until  all  the  principles  that  it  illustrates 
are  thoroughly  understood. 

First,  determine  the  direction  of  the  deflection  of  the  compass 
needle  when  the  current  flows  in  at  one  terminal  and  out  at  the 
8  65 


66 


MAGNETISM  AND  ELECTRICITY 


other  terminal  of  the  galvanoscope  coil.  To  do  this  place  the 
compass  under  the  25-turn  coil  on  the  galvanoscope,  and  turn 
the  galvanoscope  so  that  the  wire  above  the  compass  is  parallel 
to  the  needle.  Connect  one  dry  cell  to  the  binding  posts  of  the 
25-turn  coil,  and  observe  carefully  the  direction  of  the  deflection 
of  the  N  end  of  the  compass  needle.  Determine  at  which  bind- 
ing post  the  current  from  the  battery  enters  the  galvanoscope 
by  the  rule  given  in  Article  36.  Observe  to  which  binding  post 
the  carbon  rod  of  the  battery  is  connected.  The  current  leaves 
the  cell  by  this  electrode  and  returns  through  the  zinc  cup. 
Make  a  note  of  this  in  order  that  you  may  determine  the  direc- 
tion of  the  current  flow  from  the  deflection  of  the  compass 
needle. 


FIG.  51. 

Next  connect  the  solenoid  to  the  25-turn  coil  on  the  galvano- 
scope as  indicated  in  Fig.  51.  The  wires  connecting  the  solen- 
oid and  galvanoscope  must  be  at  least  4  ft.  long  so  that  the 
compass  needle  may  not  be  influenced  appreciably  by  the  bar 
magnets  to  be  used.  Place  the  two  bar  magnets  with  their  like 
poles  together.  Fasten  them  in  this  position  by  wrapping  a 
string  around  them  and  tying  it  securely.  Rubber  bands  may 
be  used  for  this  purpose. 

Thrust  one  end  of  the  bar  magnets  into  the  solenoid,  observe 
and  record  the  behavior  of  the  compass  needle.  Does  the 
needle  move?  If  so,  in  which  direction,  east  or  west?  What 
causes  it  to  move?  The  magnets  will  have  to  be  thrust  into  the 
solenoid  quickly  to  cause  appreciable  motion. 


ELECTROMAGNETIC  INDUCTION  67 

On  account  of  the  crudeness  of  the  apparatus  the  movement  of 
the  needle  may  be  very  slight.  If  the  movement  of  the  needle 
is  imperceptible,  connect  a  wire  to  the  solenoid  and  make  many 
more  turns,  or,  better  still,  make  a  short  coil  of  many  turns,  the 
more  the  better.  Connect  this  in  place  of  the  solenoid  and  try 
the  experiment.  Although  the  deflection  of  the  needle  will  not 
be  great,  it  should  be  at  least  large  enough  to  be  noticed. 

Quickly  withdraw  the  bar  magnets  and  observe  the  direction 
of  the  deflection  of  the  needle.  Repeat  this  until  you  are  certain 
of  the  results. 

From  the  direction  of  the  deflection  of  the  needle,  determine 
the  direction  of  the  current  in  the  solenoid  and  galvanoscope 
coil.  Is  the  end  of  the  solenoid  of  the  same  or  of  opposite 
polarity  as  the  end  of  the  magnet  which  was  introduced?  If  you 
cannot  tell  at  first,  repeat  the  experiment  until  you  are  sure  of 
your  answer. 

Reverse  the  bar  magnets  and  repeat  the  experiment.  In  place 
of  the  bar  magnets  use  the  horseshoe  magnet.  Place  one  pole 
inside  of  the  solenoid  and  withdraw  it  quickly.  To  prevent 
abrasion  of  the  insulation  on  the  solenoid  coil,  first  wrap  a  sheet 
of  writing  paper  around  the  solenoid  and  fasten  it  in  place  by  a 
string  or  rubber  band.  Perhaps  it  will  be  impossible  to  move 
the  horseshoe  magnet  into  the  solenoid  quickly  enough  to  cause 
a  deflection.  It  can,  however,  be  withdrawn  with  sufficient 
speed  to  cause  a  perceptible  deflection. 

Reverse  the  poles  of  the  magnet  and  repeat.  Compare  the 
results  obtained  with  the  horseshoe  magnet  with  the  results 
obtained  with  the  bar  magnets.  Prepare  a  table  for  your  data 
thus: 

TABLE  III 


Bar  magnets 

Deflection  of  N-pole  of 

compass  needle 

N-pole  moved  into  solenoid  

Toward  east  or  west, 
proper  description. 

Put  in  here  the 

^V-pole  withdrawn     

Toward  east  or  west. 

Put  in  here  the 

proper  description. 

$-pole  moved  into  solenoid  

Toward  east  or  west, 
proper  description. 

Put  in  here  the 

<S-pole  withdrawn             

Toward  east  or  west. 

Put  in  here  the 

proper  description. 

68                 MAGNETISM  AND  ELECTRICITY 
TABLE  III—  (Continued) 

Bar  magnets 

Deflection  of  JV-pole  of 

compass  needle 

Horseshoe  magnets 

N-pole   inside    of    coils;  magnet 
moved  in. 

Toward  east  or  west, 
proper  description. 

Put  in  here   the 

N-pole    inside  of  coils;    magnet 
moved  out. 

Toward  east  or  west, 
proper  description. 

Put  in  here  the 

£-pole    inside    of  coils;    magnet 
moved  in. 

Toward  east  or  west, 
proper  description. 

Put  in  here  the 

£-pole    inside    of  coils;   magnet 
moved  out. 


Toward  east  or  west.      Put  in  here  the 
proper  description. 


64.  Theory. — This  experiment  with  the  apparatus  available 
will  only  illustrate  principles,  and  even  that  not  satisfactorily 
in  every  respect  on  account  of  the  few  turns  on  the  solenoid  and 
lack  of  sensitiveness  of  the  galvanoscope.  If  a  sensitive  galvan- 
ometer were  used  in  place  of  the  galvanoscope,  measurements 
could  be  made  which  would  be  very  instructive. 

In  the  experiments  with  the  magnet  and  electromagnet  the 
student  learned  that  the  space  surrounding  a  magnet  is  permeated 
or  filled  with  a  magnetic  influence,  or  perhaps  it  would  be  better  to 
say  that  the  space  surrounding  a  bar  magnet  has  some  unique 
properties.  These  properties  we  call  magnetic,  and  we  also  call 
the  space  that  has  these  properties  a  magnetic  field. 

In  the  experiments  with  the  electromagnet  it  was  shown  that  a 
coil  carrying  an  electric  current  has  the  same  magnetic  properties 
as  a  bar  magnet;  in  short,  that  a  current-bearing  wire  is  surrounded 
by  a  magnetic  influence  and  will  magnetize  an  iron  bar.  An 
electric  current  produces  a  magnetic  field.  Conversely  it  is 
reasonable  to  expect  that  if  a  magnetic  field  be  introduced  into  a 
coil,  or  if  a  magnetic  field  is  built  up  around  a  wire,  a  current 
will  be  developed  in  the  wire.  The  results  of  experiment  18 
show  this  is  precisely  what  happens.  It  is  not  the  metal  that 
causes  the  current  in  the  solenoid,  but  the  magnetic  field  sur- 
rounding the  iron.  The  student  can  verify  this  by  trying  the 
experiment  with  an  unmagnetized  piece  of  steel  and  seeing  if  the 
needle  is  deflected. 

In  order  that  the  student  may  have  a  clear  understanding  of 
the  principles  of  the  operation  of  electrical  apparatus,  he  must 


ELECTROMAGNETIC  INDUCTION  69 

realize  that  the  magnetic  field  surrounding  a  magnet  is  the  seat 
of  the  property  or  energy  that  causes  a  current  in  the  coil. 

Furthermore,  the  results  of  the  experiment  show  that  when  the 
N-pole  of  the  bar  magnet  was  thrust  into  the  coil  the  deflection  of 
the  needle  was  in  one  direction,  and  when  the  magnet  was  with- 
drawn the  deflection  was  in  the  opposite  direction.  While  the 
bar  magnet  remained  stationary  the  compass  needle  remained 
stationary.  These  facts  show  that  the  direction  of  the  current 
is  determined  by  the  polarity  of  the  magnet  and  the  relative 
motion  between  the  coil  and  the  magnet. 

Another  important  principle  is  the  fact  that  the  motion  of  the 
bar  magnet  is  opposed  by  the  induced  current.  By  induced 
current  is  meant  the  current  developed  in  the  coil.  Careful 
observation  will  show  that  when  the  jV-pole  of  the  magnet  was 
thrust  into  the  coil,  the  current  in  the  galvanoscope  circuit  was 
in  such  a  direction  as  to  develop  an  N-pole  at  the  end  of  the  coil 
where  the  magnet  enters.  This  developed  JV-pole  opposes  the 
introduction  of  the  bar  magnet.  Again,  when  the  magnet  is 
withdrawn  the  deflection  of  the  needle  is  in  the  opposite  direction 
showing  that  the  current  has  reversed.  A  careful  inspection  of 
the  coil,  and  an  application  of  the  rule  which  gives  the  relation 
between  the  direction  of  current  and  the  magnetic  lines,  will 
show  that  the  end  of  the  coil  near  the  JV-pole  of  the  magnet  is  a 
south  pole.  This  south  pole  attracts  the  magnet  and  again 
opposes  its  motion. 

There  is  still  another  way  of  showing  that  the  induced  current 
opposes  the  motion  of  the  bar  magnet. 

Every  time  the  needle  is  deflected  from  its  position  of  rest, 
some  work  must  be  done,  or  energy  must  be  spent.  This 
energy  must  be  supplied  by  the  operator  who  thrusts  the  magnet 
into  the  coil.  But  no  energy  can  be  transferred  from  one 
system  to  another  unless  the  second  system  reacts  upon  the 
first.  This  is  merely  an  extension  of  Newton's  third  law  which  is 
usually  stated  "  action  equals  reaction,  but  is  in  opposite  direc- 
tion." A  steam  engine  running  idle  does  no  work  as  there  is  no 
opposition  to  its  motion.  The  moment  a  load  is  thrown  on,  it 
pushes  against  the  engine  just  as  much  as  the  engine  pushes 
against  it,  and  work  is  done.  Unless  there  is  a  reaction,  the 
applied  force  can  do  no  work.  Since  some  energy  must  be  trans- 
ferred from  the  operator's  hand  to  the  needle  to  cause  it  to 
deflect,  the  induced  current  must  react  against,  or  oppose,  the 


70 


MAGNETISM  AND  ELECTRICITY 


motion  of  the  magnet.  A  clear  understanding  of  this  principle 
will  help  the  student  to  understand  the  principles  of  operation  of 
electric  machinery. 

It  has  been  pointed  out  already  that  the  induced  current 
flows  only  so  long  as  there  is  relative  motion  between  the  magnet 
and  the  coil.  When  this  motion  ceases  the  current  ceases. 
There  is  thus  also  a  relation  between  the  current  induced  and  the 
speed  with  which  the  magnet  is  moved. 

65.  Law  of  Electromagnetic  Induction. — Throughout  the 
foregoing  discussion  reference  has  constantly  been  made  to 


FIG.  52. 


"  induced  current"  as  though  that  were  the  immediate  result  of 
introducing  the  bar  magnet  within  the  solenoid.  This  is  because 
the  presence  of  the  current  is  more  easily  made  apparent.  The 
immediate  result  of  the  relative  motion  between  a  magnetic 
field  and  a  coil  is  an  electromotive  force,  which,  when  the  circuit 
is  closed,  causes  a  current  to  flow.  It  is  possible  to  express  the 
value  of  this  electromotive  force  (e.m.f.)  in  terms  of  the  number 


ELECTROMAGNETIC  INDUCTION  71 

of  turns  on  the  coil,  and  the  number  of  magnetic  lines  cut  per 
second.  This  relation  we  will  now  develop. 

Fig.  52  represents  a  section  of  a  coil  and  a  permanent  bar 
magnet.  The  coil  is  shown  connected  to  a  current-detecting 
instrument.  It  will  be  observed  that,  as  the  magnet  is  moved 
into  the  coil,  the  turns  or  convolutions  of  the  coil  cut  across  the 
magnetic  lines.  Suppose  the  coil  has  only  one  turn;  every  time 
this  turn  cuts  one  magnetic  line  some  electromotive  force  is 
induced  or  developed  in  the  turn.  In  the  experiment  it  was 
shown  that  the  deflection  of  the  compass  needle  varied  with  the 
speed  with  which  the  bar  magnet  was  moved  in  and  out  of  the 
coil.  The  induced  electromotive  force  thus  depends  not  only 
upon  the  total  number  of  magnetic  lines  cut,  but  upon  the 
number  cut  per  second.  Thus  if  the  total  number  of  lines  cut  by 
the  coil  of  one  turn  in  t  seconds  is  <£  (pronounced  phi)  the  number 
cut  per  second  will  be  <i>  +t,  and  accordingly  the  electromotive 

9 

force  induced  in  one  turn  will  be  determined  by  -r-     If  the  same 

t 

number  of  lines  per  second  is  cut  by  a  second  turn,  an  exactly 
equal  e.m.f.  will  be  induced  in  that  turn,  and  as  the  two  turns  are 
connected  so  that  the  e.m.f.  induced  in  one  turn  is  added  to  that 
induced  in  the  next  turn,  the  total  e.m.f.  will  be  twice  that 
induced  in  one  turn.  Exactly  in  the  same  way  an  equal  e.m.f. 
will  be  added  for  every  additional  turn  of  the  coil.  The  total 
e.m.f.  will  then  be  equal  to  the  e.m.f.  induced  in  one  turn  multi- 
plied by  the  number  of  turns  on  the  coil.  Calling  the  total  num- 
ber of  turns  on  the  coil  N,  and  the  total  e.m.f.,  E,  we  can  represent 
this  relation  thus: 


_  Number  of  turns  X  number  of  magnetic  lines 
Time,  in  seconds 

66.  Unit  of  Induced  E.M.F.  —  The  unit  of  electromotive  force 
may  be  defined  in  two  ways.  That  is,  its  definition  may  be 
based  on  two  different  physical  phenomena.  According  to  one 
definition  the  practical  unit  of  electromotive  force  is  a  certain 
fraction  of  the  pressure  of  a  standard  cell.  This  will  be  explained 
later.  The  other  physical  phenomenon  upon  which  the  defini- 
tion is  based  is  the  rate  at  which  the  magnetic  lines  are  cut.  Thus 
when  one  turn  of  a  wire  cuts  one  magnetic  line  per  second  an 


72  MAGNETISM  AND  ELECTRICITY 

e.m.f.  of  a  definite  value  is  induced.  This  value  is  called  the 
absolute  unit  of  electromotive  force.  For  practical  purposes  this 
unit  is  too  small.  The  volt,  which  is  the  practical  unit,  is  equal 
to  the  pressure  induced  when  one  turn  cuts  100,000,000  mag- 
netic lines  per  second.  This  value,  100,000,000,  is  usually 
written  108,  which  means  10  multiplied  by  itself  8  times.  Thus 
if  it  requires  a  cutting  of  108  lines  by  one  turn  to  develop  one  volt, 
the  number  of  volts  induced  in  a  coil  of  N  turns  when  it  cuts  $ 
lines  in  t  seconds  is  then 


EXAMPLES 

Suppose  the  number  of  magnetic  lines  in  a  coil  increases  from  0  to 
800,000  in  0.02  of  a  second.  How  many  volts  are  induced  in  a  coil  of 
ten  turns? 

Solution.  — 

N  =  W 
$=800,000 
*=0.02 
Then 

10X800000 


0.02X100000000 
=  4  volts 

2.  The  magnetic  field  of  a  generator  has  a  coil  of  2,000  turns;  the  circuit 
is  suddenly  broken  so  that  the  flux  of  10,000,000  lines  decreases  to 
zero  in  3/100  second.  What  voltage  is  induced  in  the  coil? 

Solution. — 

#  =  2,000 
$>  =  10,000,000 
*=0.03 
Then 

2000X  10000000 


0.03X100000000 
2000 
=  ^^  =  6666.7  volts 


67.  The  Development  of  an  E.M.F.  by  Electromagnets. — In 

the  preceding  discussion  the  principle  of  electromagnetic  induc- 
tion was  illustrated  by  the  use  of  permanent  bar  magnets.  It  is 
not  practical  to  make  large  electric-current  generators  by  using 
permanent  magnets.  The  most  common  use  of  permanent 
magnets  for  the  induction  of  an  e.m.f.  is  the  magneto  tele- 


ELECTROMAGNETIC  INDUCTION 


73 


phone  ringer,  Fig.  17,  and  magneto-generators  for  gasoline 
engine  ignition.  Neither  one  of  these  requires  a  large  current. 
When  large  currents  are  to  be  generated,  electromagnets  are 
employed  for  supplying  the  magnetic  field.  The  fundamental 
principles  of  inducing  electric  currents  by  the  use  of  electromag- 
nets will  be  made  clear  by  the  following  experiment. 

68.  Experiment  19.    Induction  of  E.M.F.  by  Electromagnets. 
Apparatus. — 
Electromagnet 
Galvanoscope 
Dry  cells 


ARMATURE 


FIG.  53. 

Operation. — First  determine  the  relative  direction  of  the  flow 
of  current  through  the  galvanoscope  coil  and  the  direction  of  the 
deflection  of  the  JV-seeking  end  of  the  compass  needle,  in  the  same 
way  as  in  experiment  18.  Make  a  note  of  this. 

Around  the  central  portion  of  the  rectangular  armature  of  the 
electromagnet  wind  about  25  turns  of  annunciator  wire.  The 
ends  of  the  armature  must  be  left  bare  so  that  good  contact  can 


74  MAGNETISM  AND  ELECTRICITY 

be  made  with  the  electromagnet  core.  Place  the  armature 
up  against  the  electromagnet,  and  connect  the  coil  around  the 
armature  to  the  25-turn  coil  on  the  galvanoscope  as  indicated 
in  Fig.  53.  To  the  electromagnet  coil  connect  two  dry  cells  in 
series  through  the  reversing  switch.  This  connection  is  dia- 
grammed in  Fig.  53.  Close  the  switch  and  observe  the  behavior 
of  the  compass  needle. 

Determine  the  direction  of  the  current  flow  in  the  electro- 
magnet coil.  Mark  the  N-pole  of  the  electromagnet. 

From  the  direction  of  deflection  of  the  magnetic  needle  deter- 
mine the  direction  of  the  current  flow  in  the  coil  around  the  arma- 
ture. This  current  also  tends  to  magnetize  the  iron  core.  Mark 
the  end  of  the  core  that  would  be  a  JV-pole  if  the  core  were  mag- 
netized by  this  induced  current.  Does  the  induced  current  de- 
velop magnetism  in  the  same  or  opposite  direction  as  the  electro- 
magnet coil? 

Open  the  battery  circuit  suddenly  and  compare  the  resulting 
deflection  with  that  when  the  circuit  is  closed.  Determine  the 
direction  of  the  induced  current  in  the  galvanoscope  coil  when 
the  circuit  is  broken.  Is  this  direction  the  same  as  when  the 
circuit  is  closed?  Does  the  induced  current  aid  or  oppose  the 
magnetizing  effect  of  the  electromagnet  coil? 

Close  the  switch  in  the  opposite  direction  (this  reverses  the 
battery  connection)  and  repeat  the  experiment.  How  is  the 
current  in  the  solenoid  developed?  Study  carefully  all  of  the 
conditions,  and  repeat  the  experiment  until  all  of  the  principles 
are  understood. 

69.  Theory. — The  foregoing  experiment  illustrates  another 
most  important  and  fundamental  principle.  The  principle  has 
wide  application,  and,  if  any  principle  can  be  considered  more 
important  than  any  other,  the  principle  exemplified  by  this 
experiment  is  perhaps  the  most  important  in  the  realm  of  electro- 
magnetism.  The  similarity  between  the  process  of  inducing 
currents  by  electromagnets  and  permanent  magnets  must  be 
evident  to  the  student. 

In  connection  with  experiment  18  we  learned  that  when  a 
magnetic  field  is  moved  relatively  to  a  coil  of  wire,  in  such  a 
way  that  the  turns  of  the  coil  cut  across  the  magnetic  lines,  an 
e.m.f.  is  induced.  In  that  case  either  the  coil  or  magnet  is  held 
stationary  while  the  other  is  moved.  The  necessity  for  this 
nes  in  the  permanent  attachment  of  the  magnetic  field  to  the 


ELECTROMAGNETIC  INDUCTION  75 

steel  bar.  It  must  be  evident  also  that  the  necessary  condition 
for  the  development  of  an  e.m.f.  is  not  relative  motion  between 
the  coil  of  wire  and  the  iron  bar,  but  between  the  coil  and  the 
magnetic  field.  If  by  any  means  the  relative  positions  of  the  coil 
and  field  are  varied,  or  if  a  magnetic  field  is  either  built  up  within 
or  caused  to  drop  out  of  the  coil,  in  general,  an  e.m.f.  is  induced. 
Previous  experiments  have  shown  that  when  an  electric  current 
is  passed  through  a  coil  surrounding  an  iron  core,  the  iron  is 
strongly  magnetized;  that  is,  the  current  builds  up  a  magnetic 
field.  The  iron  core  of  the  electromagnet  is  magnetized  in  this 
way.  The  magnetic  lines  form  closed  curves  and  thus  pass 
through  the  iron  armature  and  its  coil.  This  is  indicated  in 
Fig.  53.  The  building  up  of  the  magnetic  lines  within  the  arma- 
ture of  the  electromagnet  produces  the  same  result  as  the  intro- 
duction of  a  permanent  magnet.  Thus  by  the  mere  building 
up  of  a  magnetic  field  within  the  core  of  a  coil  an  e.m.f.  is  induced, 
just  as  when  a  permanent  magnet  is  introduced. 

Any  change  or  variation  in  the  current  in  the  electromagnet 
coil  will  produce  a  like  change  in  the  number  of  magnetic  lines 
that  thread  through  the  armature  coil,  and  consequently  any 
variation  in  the  current  will  induce  an  e.m.f.  If  the  armature 
coil  is  closed,  the  induced  e.m.f.  will  force  a  current  through  this 
circuit  in  such  a  direction  as  to  oppose  the  building  up  of  the  mag- 
netism produced  by  the  electromagnet  coil.  Thus  in  Fig.  53, 
if  the  electromagnet  core  has  the  polarity  indicated,  the  induced 
current  will  tend  to  cause  poles  of  like  kind  on  the  armature; 
that  is,  if  the  pole  due  to  the  current  in  the  electromagnet  coil 
is  plus  or  N,  the  pole  that  the  induced  current  tends  to  produce 
adjacent  to  the  N  pole  of  the  electromagnet  core  is  also  a  JV-pole. 
This  is  indicated  in  the  figure  by  JVi,  Nz,  and  Si,  82.  This  is 
exactly  what  one  should  expect  from  the  principles  of  action 
and  reaction  explained  in  preceding  paragraphs.  This  law  that 
the  induced  e.m.f.  is  always  in  such  a  direction  that  it  opposes 
the  action  which  induces  it  is  known  as  Lenz's  law,  and  is  evi- 
dently a  particular  case  of  the  general  law  of  action  and  reaction. 

70.  Relation  between  Primary  Current  and  Induced  E.M.F. — 
That  some  definite  relation  exists  between  the  magnetizing  cur- 
rent and  induced  e.m.f.  must  be  evident;  for,  by  the  law  of  con- 
servation of  energy,  one  cannot  get  more  energy  out  of  any  trans- 
forming device  than  is  put  into  it.  The  energy  in  our  experiment 
is  put  into  the  electromagnet  coil — which  hereafter  we  shall  call 


76  MAGNETISM  AND  ELECTRICITY 

the  "  primary."  This  energy  is  transformed  by  means  of  the 
magnetic  field  and  solenoid  into  the  energy  of  an  electric  current 
within  the  coil  on  the  armature,  which  we  shall  hereafter  call  the 
"  secondary."  The  problem  to  solve  is  to  determine  the  relation 
between  the  current  in  the  primary  and  e.m.f.  induced  in  the  sec- 
ondary coil. 

In  the  discussion  on  electromagnetism  it  was  shown  that  when 
a  current  of  I  amperes  flows  through  a  coil  of  Ni  turns  surround- 
ing an  iron  core,  the  number  of  magnetic  lines  developed  is  given 
by: 

1.257 


where 

<l>  =  total  number  of  magnetic  lines 

N  =  total  number  of  turns  on  primary  coil 

/*    =  permeability  of  magnetic  circuit 

A  =  cross-sectional  area  of  primary   coil  core  in  square 

centimeters 
I   =  total  length  of  magnetic  circuit  in  centimeters 

It  has  also  been  shown  that  the  total  e.m.f.  induced  in  a  coil, 
all  of  whose  turns  cut  across  a  magnetic  field,  is  given  by 

E  (volts)  =  *fQ8 

where  N*  is  the  total  number  of  turns  in  the  secondary  winding. 
If  all  the  magnetic  lines  produced  by  the  primary  current  pass 
through  the  secondary  coil,  $  will  be  the  total  number  of  magnetic 
lines  cut  in  time  t.  This  total  flux  is  equal  to 


Putting  this  value  of  $  in  the  equation  above  we  get 

1.257  J 


ff  (volts) 


1.257 


108  ixt 


This  equation,  translated  into  words,  means  that  the  voltage 
induced  in  the  secondary,  Fig.  53,  is  equal  to  1.257  times  the  prod- 
uct obtained  by  multiplying  together  the  primary  and  secondary 
turns,  the  current,  permeability  and  cross-sectional  area  of  the 


ELECTROMAGNETIC  INDUCTION  77 

magnetic  circuit,  and  this  product  divided  by  108  times  the  length 
of  the  magnetic  circuit,  by  the  time  required  to  build  up  the  mag- 
netic field.  This  expression  also  shows  that  for  a  given  value  of 
the  primary  ampere  turns,  the  voltage  induced  in  the  secondary 
varies  with  the  number  of  secondary  turns. 

We  have  purposely  omitted  any  reference  to  the  value  of  the 
induced  current,  for  this  value  depends  upon  some  other  quanti- 
ties which  will  be  explained  later. 

EXAMPLES 

"1.  A  coarse  wire  of  500  turns  is  wound  around  an  iron  ring  whose  cross- 
sectional  area  is  10  sq.  cm.  and  mean  length  60  cm.  On  the  outside  of 
this  primary  coil  is  wound  a  secondary  coil  of  1,000  turns.  What  voltage 
will  be  induced  in  the  secondary  coil  if  the  current  in  the  primary  changes 
from  0  to  5  amperes  in  0.1  second?  Assume  the  permeability  to  be  500. 

Solution. — 

Primary  turns     Ni=5QQ 
Secondary  turns  N%  =  1,000 
Current  7  =  5  amperes 

Permeability          IJL  =  500 
Cross-section         A  =  10  sq.  cm. 
Length  of  magnetic  circuit  I  =  60  cm. 
Time,  2=0.1  sec. 

Then 

1.257X500  X  1000  X  5X500X10 

108X  60X0.1 
=  26.2  volts 

2.  What  voltage  will  be  induced  in  the  secondary  coil  mentioned  in  example 
1,  if,  when  the  current  is  7  amperes,  the  circuit  is  broken  and  the  current 
drops  to  zero  in  0.01  second? 

Solution. — 

1=7  amperes 

£  =  0.01  sec. 

Other  quantities  same  as. in  example  1. 

Then 

1.257X500X1000X7X500X10 


E 


.  108XO. 01X60 
=  366.7  volts 


These  two  examples  show  also  that  the  induced  voltage  depends  not 
alone  upon  the  primary  current  and  number  of  secondary  turns,  but  also 
upon  the  time  required  for  the  magnetism  to  be  built  up  or  to  decay. 

71.  Practical  Applications. — This  principle  of  inducing  an 
e.m.f.  by  means  of  electric  currents  has  so  many  applications 
that  it  will  be  possible  to  explain  and  illustrate  only  a  few. 


78 


MAGNETISM  AND  ELECTRICITY 


One  of  the  oldest  pieces  of  apparatus  that  operates  in  accord- 
ance with  the  foregoing  principles  is  shown  in  the  diagram  of 
Fig.  54  and  is  known  as  an  induction  coil.  The  essential  features 
of  the  induction  coil  are  nearly  the  same  as  those  of  the  electric 
bell  already  studied,  with  the  exception  that  a  second  coil  of 
many  turns  of  fine  wire  is  wound  around  the  electromagnet  core. 
Thus  in  Fig.  54  the  iron  core  N-S  is  shown  as  being  wound  with 
two  coils  of  wire,  one  heavy  and  the  other  light.  The  heavy  or 
primary  winding  is  connected  to  a  battery  B,  vibrator  A,  and 
screw  C.  As  shown  in  the  figure,  another  circuit  which  contains 
a  condenser  is  connected  to  A  and  C. 

When  the  primary  circuit  is  closed  the  current  from  the  battery 
magnetizes  the  iron  core  and  the  resulting  development  of  mag- 


A  LA  A.A  A  J\  A  h 


FIG.  54. 

netism  through  the  secondary  coil  induces  an  e.m.f.  This  e.m.f. 
is,  however,  not  very  large,  as  the  current  increases  with  compara- 
tive slowness  for  reasons  that  will  later  be  explained.  When  the 
magnetism  of  the  core  has  reached  a  sufficiently  high  value  so 
that  the  attraction  of  the  core  for  the  vibrator  A ,  which  is  made  of 
soft  iron,  is  greater  than  the  pull  on  the  spring  S,  the  circuit  is 
broken  at  C  just  as  in  the  electric  bell.  As  soon  as  the  primary 
circuit  is  broken  the  iron  core  loses  most  of  its  magnetism  and  a 
much  higher  e.m.f.  is  induced  in  the  secondary.  As  it  has  been 
shown  that  the  induced  e.m.f.  depends  upon  the  number  of  turns 
on  the  secondary  and  the  time  required  to  magnetize  or  demag- 
netize the  iron  core,  it  is  clear  that  the  greater  the  number  of 
breaks  per  second  of  the  primary  current  at  C  the  greater  will  be 


ELECTROMAGNETIC  INDUCTION 


79 


the  induced  e.m.f.  Without  going  into  details,  it  may  be  worth 
while  to  state  that  the  purpose  of  the  condenser  is  to  prevent 
excessive  sparking  at  the  contact  point  C;  and  because  it  dis- 
charges through  the  primary  in  an  opposite  direction  to  that  of  the 
current  a  greater  degree  of  demagnetization  is  obtained. 

The  current  through  the  primary  is  furnished  by  a  few  cells  of 
low  voltage,  while  the  voltage  induced  is  comparatively  very 
high,  as  it  depends  upon  the  number  of  turns  on  the  secondary 
and  the  rapidity  of  breaking  the  circuit.  The  induction  coil 
has  many  different  forms  and  is  used  very  extensively.  In  the 
form  shown  in  Fig.  54  it  is  used  for  gas  and  gasoline  engine  igni- 
tion, for  wireless  telegraphy,  and  X-ray  work. 

In  a  modified  form  it  is  used  in  telephones.  Fig.  55  shows  a 
telephone  circuit  in  which  two  induction  coils  are  shown.  As  is 
evident  from  the  diagram  the  telephone  circuit  consists  of  three 
separate  circuits.  There  is  a  local  circuit  at  each  station  consist- 


SCCOAJDAftr- 


FVttrnttr       VT£C£/r£fl 

llllll(J 


rWor/ 


FIG.  55. 

ing  of  the  battery,  transmitter,  and  primary  of  the  induction  coil. 
The  other  circuit  is  composed  of  the  two  receivers  and  the  two 
secondary  circuits  of  the  induction  coils. 

As  has  just  been  shown,  any  variation  in  the  primary  circuit 
current  induces  an  e.m.f.  in  the  secondaries.  This  induced  e.m.f. 
is  of  much  higher  voltage  than  the  voltage  of  the  primary  circuit 
and  hence  will  be  more  effective  over  a  longer  distance.  The 
induction  coil  used  in  telephone  work  has  no  vibrator  for  the  rea- 
son that  the  primary  current  is  caused  to  increase  and  decrease 
in  value  by  the  vibrations  of  the  diaphragm  of  the  transmitter. 

The  use  of  an  induction  coil  in  wireless  telegraphy  is  shown 
in  Fig.  56.  This,  of  course,  is  a  diagram  of  the  simplest  form  of 
wireless  apparatus.  For  commercial  purposes  the  apparatus  is 
much  more  complicated,  although  the  fundamental  principles 
are  the  same. 

The  apparatus  at  the  sending  station  consists  of  an  ordinary 


80  MAGNETISM  AND  ELECTRICITY 

induction  coil  TI,  a  condenser  of  variable  capacity  C\,  and  a 
second  induction  coil  Tz  which  is  also  adjustable.  Between  the 
condenser  Ci  and  the  induction  coil  T2  is  a  spark  gap  s.  The 
current  for  operating  the  induction  coil  TI  is  supplied  by  an  alter- 
nating current  generator  through  a  key  K.  The  secondary  of  the 
induction  coil  TI  charges  the  condenser  C\  until  its  pressure  rises 
high  enough  to  cause  a  spark  to  jump  across  the  air  gap  s.  This 
discharge  of  the  condenser  is  oscillatory  and  of  very  high  fre- 
quency. These  oscillations  in  the  condenser  circuit  induce  like 
oscillations  in  the  secondary  of  the  induction  coil  T%  and  the 
aerial  line. 

The  receiving  apparatus  is  much  like  the  sending  apparatus, 
with  the  exception  that  the  air  gap  is  omitted  from  the  condenser 
circuit,  and  a  condenser,  a  telephone  receiver  and  a  crystal  of 
carborundum  replace  the  generator  A. 


FIG.  56. 

The  waves  sent  out  by  the  sending  apparatus  induce  oscilla- 
tions in  the  receiving  apparatus  with  which  the  sending  apparatus 
is  tuned.  These  oscillations  induce  other  oscillations  in  the  con- 
denser circuits,  CY,  C2'  and  C3'.  The  detector  of  the  oscillations 
in  the  circuit  C3'  is  merely  a  crystal  of  carborundum  which  has  the 
property  of  permitting  the  current  to  flow  in  one  direction  only. 
The  use  of  three  adjustible  circuits  d',  C2'  and  C3'  permits  the 
picking  up  of  oscillations  of  a  given  frequency  only.  For  non- 
selective  receiving  the  circuit  C3'  is  omitted  and  the  telephone 
receiver  is  connected  directly  across  the  condenser  C2'.  The 
student  will  observe  that  in  wireless  telegraphy  induction  coils 
are  used  in  connection  with  condensers.  This  is  for  the  purpose 
of  getting  an  oscillatory  charge  and  discharge  of  high  frequency. 
This  is  not  intended  as  a  complete  exposition  of  wireless  teleg- 


ELECTROMAGNETIC  INDUCTION 


81 


raphy,  but  merely  an  exemplification  of  the  use  of  induction  coils 
in  wireless  transmission  of  messages.  The  sending  apparatus  in 
the  Arlington  Station  is  shown  in  Fig.  57. 

72.  Self  Induction. — The  fundamental  principle  of  self  induc- 
tion is  the  fact  that  whenever  there  is  relative  motion  between  a 
conductor  and  a  magnetic  field  in  such  a  way  that  the  wire  cuts 
across  the  magnetic  lines,  an  electromotive  force  is  induced  in  the 
conductor.  It  evidently  makes  no  difference  what  may  be  the 
source  of  the  magnetic  field.  It  may  be  due  to  a  permanent 
magnet,  or  to  an  electric  current. 


FIG.  57. 

The  manner  in  which  a  current  in  one  coil  induces  or  develops 
an  e.m.f.  in  another  adjacent  coil  has  just  been  explained.  The 
magnetic  field  produced  by  a  current  in  a  coil  links  with  or 
penetrates  the  coil  itself,  as  shown  in  Fig.  30.  The  cutting  of 
the  turns  of  the  coil  by  these  magnetic  lines  induces  an  electro- 
motive force  in  exactly  the  same  way  as  when  the  magnetic 
field  is  due  to  another  adjacent  coil.  There  is  this  difference, 
however,  when  a  current  in  one  coil  induces  an  e.m.f.  in  an  adja- 
cent coil,  the  induced  current  can  be  made  apparent  by  closing 


82  MAGNETISM  AND  ELECTRICITY 

the  circuit  of  the  second  coil,  when  a  current  will  flow  which  can 
be  detected.  The  presence  of  an  induced  e.m.f.  in  the  first,  or 
primary,  coil  cannot  be  made  apparent  in  this  simple  manner,  at 
least  not  while  the  primary  current  is  increasing.  It  has  been 
shown  that  the  e.m.f.  induced  in  a  secondary  coil  opposes  the 
action  of  the  current  in  the  primary  coil.  This  is  also  true  of 
the  e.m.f.  induced  within  the  primary  coil  itself. 

In  describing  the  induction  coil  it  was  pointed  out  that  the 
purpose  of  the  condenser  was  to  prevent  sparking  at  the  point 
where  the  primary  circuit  is  broken.  This  sparking  does  not 
take  place  when  the  circuit  is  closed  but  when  the  circuit  is  opened, 
as  can  be  shown  readily  by  experiment.  For  this  experiment 
the  electric  bell  can  be  used  in  place  of  the  induction  coil. 

73.  Experiment  20.    To   Study  the   Cause   of   Sparking  at 
Break  in  Circuit  of  an  Electric  Bell. 

Apparatus. — 
Electric  bell 
Three  dry  cells 

Operation. — Connect  the  three  dry  cells  and  electric  bell  in 
series.  Take  hold  of  the  clapper  and  let  it  make  contact  with 
the  screw  and  observe  carefully  that  no  spark  appears  when  the 
contact  is  made.  Break  the  circuit  quickly;  that  is,  let  the  clap- 
per swing  against  the  bell,  and  note  carefully  the  appearance  of 
the  spark  at  the  point  of  the  screw.  Repeat  this  experiment 
until  you  are  certain  that  the  spark  appears  when  the  circuit  is 
broken  and  not  when  it  is  closed.  Can  you  explain  the  cause  of 
the  spark? 

74.  Theory. — When  the  circuit  is  closed  the  current  builds 
up  the  magnetic  field,  which  in  turn  induces  an  e.m.f.     This 
induced  e.m.f.  opposes  the  sudden  rise  of  current,  hence  no  spark 
is  caused  at  the  point  of  contact.     When  the  circuit  is  broken, 
the  applied  e.m.f.  is  no  longer  effective  in  causing  a  current,  and 
the  magnetic  field  decays  or  disappears.     This  disappearance  of 
the  magnetic  field  is  also  effective  in  producing  an  e.m.f.,  but  the 
e.m.f.  induced  tends  to  cause  a  current  in  the  same  direction  as 
the  primary  current.     The  rapidity  with  which  the  magnetic 
field  disappears  and  the  number  of  turns  of  the  electromagnet 
develop  an  e.m.f.  large  enough  to  cause  a  spark  to  jump  across 
the  contact  points.     This  spark  is  due  to  the  electromotive  force 
of  self  induction  which  opposes  the  rise  of  current  when  the  cir- 
cuit is  closed,  and  tends  to  keep  the  current  flowing  when  the 


ELECTROMAGNETIC  INDUCTION 


83 


circuit  is  broken.  This  subject  of  self  induction  is  so  important 
that  we  are  justified  in  looking  at  it  from  still  another  viewpoint. 
By  this  time  the  student  should  realize  fully  that  an  electric 
wire  is  surrounded  by  a  magnetic  field,  and  that  this  field  is  built 
up  as  the  current  increases;  remains  constant  while  the  current 
remains  constant;  and  decays  with  the  decrease  of  the  current. 


40 
35 
30 

g  25 
8.20 
<  15 


01          2345678 

Hundredths  of  a  Second 
FIG.  59. 

The  building  up  of  the  magnetic  field  requires  energy  which  must 
be  supplied  by  the  current.  It  is  a  fundamental  principle  in 
mechanics  that  no  energy  can  be  transferred  to  or  stored  in  any 
mechanism,  machine  or  system,  unless  that  mechanism,  machine 
or  system,  reacts  upon  the  system  from  which  the  energy  is  to 


40 
35 
30 
25 

2° 

« 

10 

s 


\ 


\ 


01234567 

Hundredths  of  a  Second 
FIG.  60. 

be  taken.  There  can  be  no  action  unless  there  be  something 
to  act  upon  which  will,  in  its  turn,  react.  Illustrations  of  this 
law  are  numerous.  For  instance,  when  powder  explodes  in  a 
cannon,  some  of  the  energy  set  free  by  the  explosion  is  transferred 
to  the  cannon  ball.  If  the  cannon  ball  did  not  tend  to  prevent 


84  MAGNETISM  AND  ELECTRICITY 

or  confine  the  explosion,  no  energy  would  be  stored  in  it.  Again, 
when  the  cannon  ball  strikes  a  wall,  the  energy  of  the  ball  is 
transferred  to  the  brick  or  stones  which  impede  its  progress. 
The  air  through  which  the  ball  passes  gets  relatively  little  of  the 
energy  as  it  offers  comparatively  little  resistance  to  the  motion 
of  the  ball. 

Since  it  requires  energy  to  build  up  a  magnetic  field,  or,  in  other 
words,  since  the  magnetic  field  is  a  seat  of  energy,  the  magnetic 
field  must  react  against  the  current  producing  it.  This  reaction 
is  made  apparent  by  the  retardation  in  the  growth  of  the  current. 
The  stronger  the  magnetic  field,  or  the  greater  the  number  of 
turns  of  wire  on  the  coil,  the  more  slowly  will  the  current  increase. 
Fig.  59  is  a  curve  showing  the  growth  of  a  current  in  a  coil  that 
has  considerable  self  inductance.  The  greatest  current  that  can 
flow  in  the  circuit  is  36.67  amperes,  but  the  current  does  not 
reach  this  value  until  0.8  second  after  the  closing  of  the  circuit. 
At  the  end  of  0.1  second  the  current  is  only  about  17.5  amperes. 
When  the  circuit  is  opened  the  current  does  not  immediately 
drop  to  zero,  but  decreases  gradually,  as  shown  in  Fig.  60. 

75.  Analogies. — The  effect  of  self  induction  in  preventing  the 
sudden  increase  or  decrease  of  a  current  may  be  considered  as 
analogous  to  the  action  of  the  inertia  of  a  flywheel  of  an  engine. 
When  the  steam  is  first  admitted  to  the  cylinder,  the  speed  of  the 
flywheel  increases  gradually.  Even  if  the  throttle  or  steam  pipe 
were  fully  opened,  the  speed  of  the  flywheel  would  not  suddenly 
jump  from  stand-still  to  full  speed. 

While  the  speed  of  the  flywheel  is  increasing,  the  flywheel  is 
pushing  against  the  pressure  of  the  steam,  and  the  energy  of  the 
steam  is  being  transferred  to  the  flywheel.  Only  by  reacting 
against  the  steam  pressure  can  this  energy  be  transferred.  This 
reaction  prevents  a  sudden  increase  in  the  speed. 

When  the  flywheel  has  acquired  full  speed,  and  the  speed  has 
become  constant,  a  pressure  only  sufficient  to  overcome  friction 
is  necessary,  and  no  more  energy  is  being  absorbed  or  taken  up  by 
the  wheel. 

If  the  steam  be  shut  off  suddenly,  the  engine  will  not  come  to  a 
sudden  stop,  but  the  energy  that  has  been  stored  in  the  flywheel 
will  keep  it  running  in  the  same  direction  for  some  time.  The 
motion  will  continue  until  all  of  the  energy  stored  in  the  flywheel 
has  been  returned  to  the  driving  mechanism  of  the  engine  and 
dissipated  as  heat. 


ELECTROMAGNETIC  INDUCTION  85 

76.  Self  Inductance.—  The  properties  of  the  coil  that  cause 
an  electromotive  force  to  be  induced  in  it  when  a  current  in- 
creases or  decreases  is  called  self  inductance.  This  property 
depends  upon  the  number  of  turns  on  the  coil  and  the  presence 
of  iron  within  the  circuit.  The  value  of  this  property  when  a 
change  of  1  ampere  per  second  induces  1  volt  in  the  circuit, 
is  the  unit  of  self  inductance  and  is  called  the  henry.  This 
value  of  the  self  inductance  of  a  coil  in  terms  of  the  number  of 
turns  and  permeability  of  the  magnetic  circuit,  can  be  calcu- 
lated readily.  We  showed  that  when  a  current  of  I  amperes 
flows  through  a  coil  of  N  turns,  if  the  coil  is  a  long  solenoid,  the 
field  strength  within  the  solenoid  is  given  by 

1.257XJV7 

H  =      ~T~ 

If  the  coil  has  an  iron  core  of  cross-sectional  area  A  and  permea- 
bility M,  the  total  number  of  magnetic  lines  is  given  by 

1  .  257  'N  'In  A 
*  —    — 

We  have  also  shown  that  when  a  magnetic  field  is  built  up 
within  a  coil,  the  electromotive  force  induced  is  proportional  to 
the  rate  at  which  the  field  is  built  up,  usually  expressed  as  the 
rate  at  which  the  magnetic  lines  are  cut  by  the  turns  of  the  coil. 
The  coil  is  assumed  to  have  N  turns,  and  if  the  field  is  built  up 
in  t  seconds,  the  voltage  induced  will  be 

1.257  A7/i  A 


1.  257  WV  A  I 


.  . 

For  any  given  coil  the  quantity       ~i~A8  —  "  ls  approximately 

constant  and  is  the  value  of  E  in  volts  when  7,  the  current,  is 
1  ampere,  and  t,  the  time  required  for  the  current  to  change  1 

1.257AV1  • 
ampere,  is  1  second.     This  constant  value  -  ~~T?\SJ  --  ls  usu~ 

ally  represented  by  the  letter  L.     Thus 


and  is  called  the  inductance  of  the  coil.     It  must  be  noted  that 
this  quantity  depends  solely  upon  the  physical  properties  of 


86  MAGNETISM  AND  ELECTRICITY 

the  coil,  and  not  upon  the  current  flowing  in  the  coil.  The  e.m.f. 
induced,  or  the  e.m.f.  of  self  induction,  depends  not  only  upon 
the  value  of  the  inductance  of  the  coil,  but  also  upon  the  rate 

at  which  the  current  in  the  coil  is  changing;  that  is,  upon  -' 
Representing  the  value  of  self  inductance  by  L  we  may  write  the 
expression  for  the  induced  pressure  by  E  =  LX — 7 —  In  this 

expression  I\  expresses  the  current  at  the  beginning  and  /2  the 
current  at  the  end  of  some  interval  of  time,  and  t  represents  the 
time  during  which  the  current  changes  from  I\  to  /2. 

The  value  of  L  calculated  in  accordance  with  the  expression 

1.257ATVA 
108Z 

is  true  only  for  very  long  solenoids  or  for  coils  wound  Upon  an 
iron  core  which  forms  a  complete  magnetic  circuit.  It  may, 
however,  be  used  to  obtain  the  approximate  value  of  the  induc- 
tance of  shorter  sloenoids. 

EXAMPLES 

1.  A  solenoid  100  cm.  long,  12.567  sq.  cm.  in  cross-section,  without  iron,  is 
wound  with  2,620  turns.     What  is  its  inductance? 

Solution. — Since  the  solenoid  has  no  iron  core  /x,  the  permeability 

"1  L=;«^  :,: 

#  =  2,620 

A  =12. 567  sq.  cm. 

I   =  100  cm. 

r   1 . 257  X  2620  X  2620X12. 567 

10*  X 100 
=  0.01  henry 

2.  A  coil  of  2,000  turns  is  wound  upon  a  cast-rion  ring  whose  cross-section 
is  5  sq.  cm.  and  mean  length  40  cm.     If  the  permeability  of  the  ring  is 
1,250  what  is  the  inductance  of  the  coil? 

Solution. — 
L  = 


Then        L  = 


1QH 

#  =  2,000 
A  =5  sq.  cm. 
M  =1,250 
I   =40  cm. 

1.257X2000X2000X5X1250 


108X40 
=  7.85  henrys 


ELECTROMAGNETIC  INDUCTION  87 

3.  What  will  be  the  electromotive  force  of  self  induction  in  example  2,  if 
the  current  changes  from  0  to  5  amperes  in  1/10  second? 

Solution.  —  It  was  shown  that  the  e.m.f.  of  self  induction  is  equal  to 
,  the  inductance  times  the  rate  of  change  of  current.  The  inductance 
of  the  coil  in  example  2  is  7.85  henrys,  and  if  the  current  changes 
from  0  to  5  amperes  in  1/10  second  it  is  changing  at  the  rate  of  50 
amperes  per  second;  hence, 

#  =  7.85X50  =  392.  5  volts 
or,  according  to  formula, 
L=785 

/1=0 

72  =  5 
t  =  1/10  sec. 

Then     E  =  L^- 


The  negative  sign  merely  shows  that  the  induced  pressure  opposes 
the  flow  of  current. 

77.  Practical  Applications.  —  Self  induction  does  not  play  a 
very  prominent  part  in  direct-current  circuits,  as  it  acts  only 
while  the  current  is  changing.  The  time  required  for  the  effects 
of  self  induction  to  disappear  in  direct-current  circuits  is  also,  as 
a  rule,  very  brief;  hence  in  calculating  direct-current  circuits 
self  induction  usually  is  neglected. 

In  breaking  the  field  circuit  of  a  dynamo  the  effect  of  self 
induction  may  sometimes  have  a  serious  result.  If  the  current 
is  broken  suddenly  the  e.m.f.  of  self  induction  may  reach  a  very 
high  value,  and  if  the  insulation  is  weak,  it  may  be  punctured  and 
a  short  circuit  result.  It  is  thus  advisable  to  have  the  field  circuit 
closed  through  a  relatively  high  resistance  thus  permitting  the 
discharge  of  the  field  without  damage.  When  lifting  magnets, 
similar  to  the  one  shown  in  Fig.  44,  were  first  used,  the  circuit  was 
closed  and  opened  by  an  ordinary  double-pole  switch.  The 
inductive  arc  burned  away  the  contacts  very  rapidly.  It  is  now 
customary  to  provide  a  discharge  resistance  which  is  connected 
to  the  electromagnet  coil  by  a  switch  of  special  design,  when  the 
circuit  is  opened. 


88  MAGNETISM  AND  ELECTRICITY 

RECAPITULATION 

1.  Electromagnetic  induction  is  the  principle  of  developing  an  electro- 

motive force  whenever  the  number  of  magnetic  lines  linking  a  cir- 

cuit is  changed. 
2    The  electromotive  force  induced  in  a  conductor  when  it  cuts  across 

a  magnetic  field  is  proportional  to  the  number  of  magnetic  lines  cut 

per  second. 

3.  The  electromotive  force  induced  in  a  coil  of  N  turns  when  a  flux 

<£> 

of  $  lines  is  changed  in  it  in  t  seconds  is  given  by  E  =  N~. 

4.  The  practical  unit  of  electromotive  force  is  the  volt  and  is  the  electro- 
motive force  induced  in  a  conductor  when  it  cuts  100,000,000  which 
=  108  magnetic  lines  per  second. 

5.  The  approximate  value  of  the  electromotive  force  induced  in  the 
secondary  of  an  induction  coil  is  given  by 

.. 

volts 


where  NI  =  primary  turns 

N2  =  secondary  turns 

/  =  change  in  current  in  t  seconds 

n  =  permeability 

A  =  cross-sectional  area  of  magnetic  circuit. 

6.  Self  induction  is  the  principle  of  developing  an  electromotive  force 
within  a  conductor  by  the  current  within  the  same  conductor. 

7.  Mutual  induction  is  the  principle  of  developing  an  electromotive 
force  in  a  conductor  when  a  current  varies  in  an  adjacent  conductor. 

8.  Self  inductance  is  the  property  of  a  coil  which  determines  the  value 
of  the  electromotive  force  of  self  induction  when  the  current  changes 
at  the  rate  of  1  ampere  per  second. 

9.  The  unit  of  inductance  is  the  henry,  usually  symbolized  by  the  letter 
L,  and  is  defined  as  that  inductance  which  develops  an  electromotive 
force  of  1  volt  when  the  current  changes  at  the  rate  of  1  ampere  per 
second. 

10.  Owing  to  the  property  of  inductance,  a  current  does  not  instantly 
rise  to  its  maximum  value  in  a  coil,  nor  when  the  circuit  is  broken 
does  it  instantly  drop  to  zero. 

11.  The  approximate  value  of  the  inductance  of  a  coil  is  given  by 

L257VW 


CHAPTER  V 
CURRENT  ELECTRICITY 

78.  Introduction. — The    method    of    developing    an    electric 
current  by  electromagnetic  induction  has  been  briefly  discussed 
and   experimentally   illustrated.     For   operations   that   require 
comparatively   large   currents,   the   electromagnetic  process  of 
current  generation  is  usually  used  either  directly,  or  indirectly 
by  first  charging  a  storage  battery,  and  then  using  this  as  the  source 
of  current.     The  simple  primary  cell  will  serve,  however,  to 
furnish  an  electric  current  whose  properties  we  shall  now  study. 
At  the  same  time  we  are  going  to  determine  some  of  the  main 
and  most  obvious  characteristics  of  the  simple  cell. 

79.  Experiment  21.    The  Simple  Voltaic  Cell. 
Apparatus. — 

Strip  of  zinc 

Strip  of  copper 

Dilute  sulphuric  acid 

Tumbler 

A  small  quantity  of  mercury 

Connectors  and  holder 

Operation. — Procure  about  1  oz.  of  pure  sulphuric  acid  at 
a  drug  store  and  dilute  this  with  water.  The  necessary  degree 
of  dilution  is  obtained  by  pouring  one  part  of  the  acid  into  twenty 
parts  of  water.  Rain  water  will  be  the  best.  Always  pour  the 
acid  into  the  water;  never  the  water  into  the  acid.  Be  careful 
not  to  get  any  of  the  pure  or  dilute  acid  upon  the  hands  or  clothes; 
also  never  leave  it  in  the  tumbler  where  some  one  may  accident- 
ally drink  it. 

Take  a  strip  of  zinc  and  place  it  in  a  tumbler  of  dilute  sulphuric 
acid.  After  a  short  time  it  will  be  observed  that  bubbles  of  gas 
are  produced  at  the  surface  of  the  zinc  and  rise  to  the  surface  of 
the  liquid.  These  are  hydrogen  bubbles  and  are  due  to  the  action 
of  the  acid  upon  the  zinc.  The  acid  combines  with  the  zinc, 
producing  zinc  sulphate  and  giving  off  hydrogen. 

After  the  zinc  has  been  in  the  acid  for  a  short  time  take  it  out 
10  89 


90 


MAGNETISM  AND  ELECTRICITY 


CO/=>/=£/? 


ZJNC 


and  with  an  old  tooth  brush  or  cloth  rub  some  mercury  over  both 
sides  of  the  zinc.  Take  only  a  small  drop  of  mercury  for  this. 
When  you  rub  the  mercury  on  the  zinc  lay  the  zinc  on  a  flat 
surface.  Notice  that  mercury  combines  with  the  zinc,  produc- 
ing a  bright  surface.  Coating  zinc  with  mercury  is  called  amal- 
gamation. 

Put  the  amalgamated  strip  of  zinc  into  the  dilute  acid  and  again 
observe  the  action.  Does  the  acid  attack  the  zinc  as  readily  as 
before? 

Replace  the  zinc  by  a  strip  of  copper  and  observe  the  action  of 

the  acid.  Do  you  see  any  bub- 
bles collecting  on  the  copper  and 
rising  to  the  surface? 

Next  fasten  the  zinc  and  cop- 
per strips  into  the  holder  and  dip 
both  into  the  dilute  acid  as 
shown  in  Fig.  61.  Connect  a 
wire  about  1  ft.  long  to  one 
binding  post.  Touch  the  other 
binding  post  with  the  other  end 
of  the  wire  and  notice  whether 
bubbles  arise.  Connect  the  loose 
end  of  the  wire  to  the  other 
binding  post  and  observe  the 
action  in  the  cell. 

From  which  electrode  do  most 
of  the  bubbles  arise?     Discon- 
nect the  wire  from  one  binding  post  and  notice  if  bubbles  continue 
to  rise.    Connect  the  wires.     Do  bubbles  rise? 

80.  Theory. — The  student  has  observed  that  sulphuric  acid 
attacks  the  unamalgamated  zinc,  but  that  when  the  zinc  is  amal- 
gamated the  chemical  action  almost  entirely  ceases.  The  copper 
is  not  attacked  by  the  acid  to  an  appreciable  extent.  When  the 
zinc  strip  alone  is  in  the  acid  the  energy  liberated  by  the  chemical 
action  is  all  converted  into  heat.  If  the  strip  had  been  left  in  the 
acid  for  some  time  the  electrolyte  would  have  rapidly  increased 
in  temperature.  Amalgamation  almost  entirely  eliminated  the 
chemical  action. 

The  cause  of  the  appearance  of  the  hydrogen  bubbles  at  the 
surface  of  the  unamalgamated  zinc  when  dipped  into  dilute  sul- 
phuric acid  is  that  weak  electrical  currents  are  set  up  between  the 


FIG.  61. 


CURRENT  ELECTRICITY  91 

zinc  and  the  impurities  in  it — carbon  or  iron  particles.  If  the 
zinc  is  pure  these  local  currents  cannot  be  set  up,  and  consequently 
no  hydrogen  bubbles  appear.  Amalgamating  the  zinc  stops  this 
so-called  local  action,  because  the  mercury  coats  the  impurities 
while  it  dissolves  the  zinc.  It  is  important,  therefore,  to  amal- 
gamate the  zinc  to  prevent  its  wasting  away  while  the  cell  is  on 
open  circuit.  The  zinc  is  under  all  circumstances  consumed  when 
the  current  is  flowing.  Amalgamation  serves  only  to  preserve 
the  zinc  when  the  circuit  is  open. 

When  both  the  zinc  and  copper  strips  are  immersed  in  the  acid 
and  the  outside  terminals  of  the  electrodes  are  joined  by  a  copper 
wire,  the  chemica  action  again  takes  place.  Hydrogen  bubbles 
rise  from  the  copper  plate  and  the  bubbles  of  another  gas  rise 
from  the  zinc  electrode.  If  a  thermometer  is  placed  in  the 
electrolyte  it  will  be  observed  that  the  temperature  rises  much 
more  slowly  than  when  the  unamalgamated  zinc  alone  is  used. 
The  energy  of  chemical  action  is  no  longer  being  converted  into 
heat,  as  previously,  but  when  the  proper  test  is  made  it  will  be 
found  that  an  electric  current  is  flowing.  Some  of  the  chemical 
energy  is  converted  into  electrical  energy,  which  is  again  con- 
verted into  heat  in  the  electrodes,  wire,  and  electrolyte. 

81.  Definitions. — A  voltaic  cell  is  the  combination  of  electrolyte, 
electrodes,   and  container.     More  than  one  cell  connected  to- 
gether is  called  a  battery. 

A  conductor  is  any  material  along  which  a  current  of  electricity 
will  flow.  The  connecting  wire  used  in  the  foregoing  experiment 
is  a  conductor.  All  conductors  are  however  not  metallic;  for  in- 
stance the  dilute  acid  is  also  a  conductor.  Conductors  may  thus 
be  either  solid  or  liquid.  The  conduction  is,  however,  not  the  same 
in  the  two  cases.  Solid  conductors  as  a  rule  transfer  electricity 
without  undergoing  any  change  or  decomposition.  Liquids 
as  a  rule  are  decomposed,  when  a  current  of  electricity  is  passed 
through  them.  This  is  not  true  in  every  case,  as  for  instance  in 
mercury. 

82.  Volt-ammeter. — The  student  will  hereafter  use  the  instru- 
ment shown  in  Fig.  62  in  place  of  the  galvanoscope  for  detecting 
an  electric  current.     This  instrument  is  a  combined  voltmeter 
and  ammeter  and  hence  is  called  a  volt-ammeter.     The  general 
principle  of  operation  of  this  instrument  is  readily  understood. 
The  deflection  is  produced  by  the  interaction  of  the  magnetic 


92  MAGNETISM  AND  ELECTRICITY 

field  produced  by  the  electric  current  flowing  through  a  coil  of 
fine  wire  mounted  so  as  to  rotate  in  the  air  gap  of  a  permanent 
magnet,  and  the  magnetic  field  due  to  this  permanent  magnet. 
Both  the  coil  and  magnet  poles  are  visible  through  the  window 
in  the  cover  of  the  instrument.  The  instrument  is  thus  in  prin- 
ciple much  the  same  as  the  galvanoscope  with  this  difference. 
On  the  galvanoscope  the  coil  is  fixed  and  the  compass  needle, 
which  is  a  permanent  magnet,  is  forced  to  turn  by  the  action 
of  the  magnetic  field  due  to  the  coil.  The  deflection  of  the  needle 
is  indicated  in  degrees. 


FIG.  62. 

In  the  volt-ammeter  the  permanent  magnet  is  fixed  and  the 
coil  is  mounted  on  a  spindle  so  that  it  can  rotate,  its  motion  being 
controlled  by  a  coiled  spring.  The  graduations  of  the  scale  are  in 
volts  and  amperes  instead  of  degrees.  These  differences  make  the 
instrument  more  sensitive,  accurate,  and  convenient. 

Since  this  is  the  first  time  that  the  student  is  asked  to  use  a 
delicate  instrument,  some  instruction  for  its  use  will  be  given. 
First  examine  the  volt-ammeter  and  observe  that  it  has  3  binding 
posts,  one  marked  + ,  the  one  next  to  it  marked  A ,  and  the  third 
marked  V.  In  connecting  this  instrument  to  a  circuit  always 


CURRENT  ELECTRICITY 


93 


connect  the  +  post  to  the  wire  that  is  connected  to  the  carbon, 
copper,  or  positive  terminal  of  the  cell  or  other  source  of  e.m.f. 
Never  connect  the  post  A  to  the  zinc  terminal  of  a  cell  unless  some 
resistance  is  included  in  the  circuit.  If  you  should  connect  a  dry 
cell  directly  to  posts  +  and  A,  the  current  through  the  instrument 
may  be  too  large  and  the  instrument  may  be  damaged.  While 
one  cell  alone  may  not  cause  serious  trouble,  more  than  one 
undoubtedly  will  cause  damage.  Never  connect  this  instrument 
to  a  house-lighting  circuit.  The  meter  is  not  designed  for  such 
use,  and  if  so  connected  it  will  undoubtly  be  burned  out.  Follow 
the  instructions  carefully  and  you  will  have  no  trouble. 


FIG.  63. 

83.  Experiment  22.     Electromotive  Force  or  Pressure. 

Apparatus. — 
Volt-ammeter 
Simple  voltaic  cell 
Dry  cell 

Operation. — Connect  the  positive  terminal  of  the  simple  vol- 
taic cell  to  the  +  binding  post  of  the  volt-ammeter  by  means  of  a 
short  piece  of  copper  wire.  Connect  the  other  cell  electrode  to 
the  binding  post  marked  V.  When  the  connections  are  made  as 
indicated  in  Fig.  63,  observe  and  record  the  deflection.  What 
causes  the  pointer  to  move? 
Disconnect  the  voltaic  cell  and  connect  one  dry  cell  to  the  volt- 


94 


MAGNETISM  AND  ELECTRICITY 


ammeter  in  the  same  way,  and  again  observe  and  record  the 
deflection. 

84.  Theory. — The  student  learns  from  the  foregoing  experiment 
that  different  cells  cause  different  deflections  of  the  voltmeter. 
The  cause  of  the  deflection  is  a  current  of  electricity  which  flows 
through  the  movable  coil  of  the  voltmeter.  Naturally  the  stu- 
dent will  ask,  what  causes  the  current  to  flow?  This  question  is 
more  easily  answered  by  analogy  than  directly. 

Experience  shows  that  water  flows  through  pipes  from  points 
of  higher  to  points  of  lower  mechanical  pressure,  and  to  raise 
water  through  a  pipe  requires  pressure.  By  analogy  we  say  that 


FIG.  64a. 

electricity  is  transferred  from  points  of  higher  to  points  of  lower 
electrical  pressure.  The  action  in  a  cell  may  be  considered  analo- 
gous to  the  action  of  a  pump  in  a  water  circuit.  At  the  zinc 
electrode  the  pressure  rises,  forcing  the  electricity  toward  the 
copper  through  the  electrolyte.  At  the  copper  electrode  there  is 
another  increase  in  pressure  so  that  the  copper  electrode  is  at  the 
highest  electrical  pressure  in  the  circuit.  This  is  represented  in 
the  diagram  of  Fig.  64a.  This  is  a  diagram  which  attempts  to 
represent  the  action  in  the  cell.  Between  the  zinc  plate  and  the 
acid  solution  there  is  a  sudden  rise  in  pressure  of  0.52  unit,  so  that 
the  pressure  of  the  zinc  sulphate  solution  next  the  zinc  plate  is  rep- 
resented by  the  point  B.  Then  follows  a  drop  in  pressure  through 


CURRENT  ELECTRICITY 


95 


the  cell  until  the  copper  electrode  is  reached,  when  another  rise  of 
pressure  occurs.  This  rise  is  about  0.58  unit.  The  pressures  at 
the  copper  sulphate  and  copper  electrode  are  represented  by 
points  C  and  D  respectively.  From  the  copper  plate  the  pressure 
falls  off  uniformly  along  the  external  circuit,  until  the  zinc  plate  is 
again  reached.  To  complete  the  analogy,  the  figure  should  be 
considered  as  wound  upon  the  surface  of  a  cylinder  so  as  to  make 
Ai  coincide  with  A.  This  is  shown  in  Fig.  64b.  The  cause  of 
the  flow  of  electric  current  is  called 
electromotive  force,  or  in  practice 
pressure  or  voltage.  This  pressure 
is  in  some  way  due  to  the  chemical 
action  in  a  cell.  In  a  generator  it 
is  produced  in  another  way  as  will 
be  shown. 

The  absolute  value  of  the  pres- 
sure developed  in  a  cell  depends 
upon  the  material  of  which  the  cell 
is  made.  This  is  shown  by  the  fact 
that  the  voltmeter  deflection  is  less 
when  the  simple  voltaic  cell  is  con- 
nected than  with  the  dry  cell. 
Other  illustrations  of  this  will  be 
given  later. 

The  student  must  not  confuse 
pressure  with  current.  The  current 
that  a  given  cell  will  give  depends 
upon  several  things,  but  the  pres- 
sure or  electromotive  force  is  deter- 
mined by  the  materials  of  which  the 
cell  is  made.  Many  different  substances  can  be  used  for  this  pur- 
pose, but  in  every  case  the  action  of  the  electrolyte  must  be  greater 
on  one  substance  than  on  the  other.  For  the  negative  electrode 
zinc  is  almost  invariably  used  in  commercial  voltaic  cells. 

Volt. — The  unit  of  electrical  pressure  is  called  the  volt.  Numer- 
ically it  is  about  equal  to  the  pressure  of  the  simple  voltaic  cell, 
when  fresh,  with  copper  and  zinc  as  electrodes  and  dilute  sul- 
phuric acid  for  the  electrolyte.  It  is  defined  as  fjffinnr  of  the 
pressure  of  a  Weston  standard  cell.  This  is  a  voltaic  cell  made 
according  to  certain  definite  specifications  from  materials  of  known 
degrees  of  purity.  Electrical  pressures  are  expressed  in  volts. 


FIG.  64b. 


96  MAGNETISM  AND  ELECTRICITY 

85.  Expenditure  of  Energy  in  a  Circuit. — It  has  been  pointed 
out  that  when  the  external  circuit  is  opened  the  energy  of  chemical 
action  that  does  take  place  is  transformed  into  heat  within  the 
cell.     When  the  zinc  has  been  properly  amalgamated,  practically 
no  chemical  action  takes  place  within  the  simple  voltaic  cell  just 
described.     When  the  external  circuit  is  closed  the  chemical 
action  begins  and  continues  so  long  as  the  current  flows.     In  order 
that  a  current  may  flow  continuously  a  difference  of  electrical 
pressure  must  be  maintained  between  any  two  points  of  the  cir- 
cuit.    The  maintenance  of  this  difference  of  electrical  pressure 
requires  a  continuous  expenditure  of  energy,  and  hence,  continu- 
ous chemical  action  in  the  cell. 

86.  Experiment  23.     To  Study  Polarization. 
Apparatus. — 

Volt-ammeter 

Simple  voltaic  cell 

Operation. — First  clean  the  copper  electrode  of  a  simple  cell 
with  a  piece  of  fine  sandpaper;  connect  the  simple  voltaic  cell  to 
the  voltmeter  terminals  as  in  Fig.  63.  Close  the  switch  at  a  defi- 
nite time  and  read  the  voltmeter  deflection  at  first  every  ten  sec- 
onds, later  at  longer  intervals.  Keep  the  circuit  closed  for  fifteen 
minutes. 

Next  remove  the  copper  electrode  from  the  solution  and  rub  off 
the  hydrogen  bubbles  under  water.  Also  remove  and  clean  the 
zinc.  Replace  the  electrodes  and  take  a  new  series  of  observations 
for  fifteen  minutes.  Does  the  deflection  fall  off  more  or  less 
rapidly  than  in  the  first  part  of  the  experiment?  Why  does  the 
deflection  of  the  voltmeter  decrease  with  time? 

87.  Theory. — It  is  of  course  clear  that  the  deflection  of  the  volt- 
meter is  caused  by  an  electric  current  whose  source  is  the  cell. 
The  deflection  varies  as  the  current  strength  changes.     Any  de- 
crease in  the  current  will  be  accompanied  by  a  decreased  deflection. 
It  was  noted  in  experiment  21  that  gas  bubbles  arose  from  the 
copper  electrode,  when  the  two  electrodes  were  connected.     These 
gas  bubbles  first  collect  on  the  electrode  and  greatly  increase  the 
resistance  of  the  cell.     Any  increase  in  the  resistance  decreases 
the  current  and  consequently  the  deflection. 

The  e.m.f.  of  a  cell  is  subject  to  changes  produced  by  the  cur- 
rent flowing  through  the  cell.  These  changes,  the  causes  of 
which  are  many,  are  called  polarization  and  since  they  tend  to 
decrease  the  current  the  effect  is  called  the  counter  e.m.f.  of  polar- 


CURRENT  ELECTRICITY  97 

ization.  This  counter  e.m.f.  must  always  be  subtracted  from 
the  original  e.m.f.  in  order  to  get  the  resultant  e.m.f.  of  the  cell. 
In  all  calculations  of  electrical  quantities  in  a  circuit  containing  a 
cell  this  resultant  e.m.f.  and  not  the  original  e.m.f.  should  be  used. 

In  addition  to  an  increase  in  resistance  the  hydrogen  bubbles 
also  create  a  counter  pressure  tending  to  drive  the  current  in  the 
opposite  direction.  These  tw^  effects  together  are  called  polar- 
ization. Thus  in  nearly  every  case,  polarization  in  a  voltaic  cell 
is  due  to  hydrogen  bubbles  collecting  on  the  positive  electrode. 

Deposition  on  the  electrodes  of  a  substance  different  from  that 
of  the  plates  is  one  of  the  main  factors  of  polarization.  This  is 
very  apparent  in  the  simple  voltaic  cell,  consisting  of  a  zinc  and  a 
copper  plate  in  dilute  sulphuric  acid.  When  the  circuit  is  closed, 
zinc  goes  into  solution  and  hydrogen  collects  on  the  copper  plate 
increasing  the  resistance  and  developing  a  counter  pressure. 

88.  Kinds  of  Cells. — Cells  are  ordinarily  classified  as  primary 
and  secondary.     A  primary  cell  is  one  in  which  the  electrical 
energy  is  produced  by  the  chemical  action  which  destroys  one 
of  the  plates.     This  chemical  action  does  not  have  to  be  preceded 
by  electrolysis,  but  takes  place  immediately  upon  the  assembly- 
ing  of  the  parts  of  the  cell  and  the  closing  of  the  circuit. 

The  secondary,  or  storage,  cell  is  one  in  which  the  chemical 
action  producing  the  current  must  be  preceded  by  electrolysis. 
That  is,  before  an  electric  current  can  be  drawn  from  the  cell  the 
chemical  condition  of  the  plates  must  first  be  changed  by  send- 
ing a  current  of  electricity  through  the  cell  in  a  direction  opposite 
to  that  of  the  current  given  out  by  the  cell.  This  process  is 
called  charging.  Storage  cells  will  be  explained  in  connection 
with  the  chapter  on  electrolysis.  Primary  cells  may  conveniently 
be  classified  as  single-fluid  and  two-fluid  cells.  That  is,  if  the 
electrolyte  is  only  one  kind  of  a  liquid  and  both  electrodes  are 
immersed  in  it,  then  the  cell  belongs  to  the  first  class.  When 
each  electrode  is  immersed  in  a  separate  liquid  the  cell  belongs 
to  the  second  class.  This  classification  is  for  convenience  only, 
and  does  not  in  any  way  represent  a  different  method  of  gener- 
ating or  producing  electrical  current. 

89.  One-fluid  Cells. — The  most  common  single-fluid  cell  was 
devised  by  Leclanche,  and  consists  of  two  forms.     One  form  is 
shown  in  Fig.  65  and  is  the  one  commonly  called  the  Leclanche 
cell.     The  essential  parts  of  the  Leclanche  cell  are  a  carbon  rod 
for  the  positive  electrode,  a  zinc  rod  for  the  negative  electrode,  a 


98 


MAGNETISM  AND  ELECTRICITY 


solution  of  ammonium  chloride  for  the  electrolyte,  and  a  glass 
jar.  The  carbon  rod  is  placed  in  a  porous  earthenware  cup 
packed  in  a  mixture  of  manganese  dioxide  and  coke.  The 
electromotive  force  of  this  cell  ranges  from  1.4  to  1.7  volts  on 
open  circuit.  The  manganese  dioxide  is  used  as  a  depolarizer. 
The  hydrogen  on  its  way  to  the  carbon  plate  is  oxidized  by  the 
oxygen  of  the  black  oxide  of  manganese.  Even  with  a  depo- 
larizer, the  cell  polarizes  very  rapidly  and  is,  therefore,  suited 
only  for  open  circuit  work;  that  is,  for  such  work  as  the  ringing 
of  door  bells.  The  other  form  of  the  Leclanche  cell  is  ordinarily 
called  the  dry  cell.  In  this  form  the  carbon  rod  is  in  the  center 
of  a  zinc  cup.  The  cup  acts  as  the  negative  electrode.  The 


carDon 

• zinc 


porous 
cup 


- 

$g 

i 


t 


4Z//VC 


FIG.  65. 


FIG.  66. 


electrolyte  is  in  the  form  of  a  paste  of  zinc  oxide,  zinc  chloride, 
ammonium  chloride,  plaster  of  Paris,  and  water.  To  prevent 
evaporation,  the  cell  is  sealed  with  wax  or  some  other  cheap 
impervious  matter.  The  electromotive  force  of  the  dry  cell 
is  about  1.4  volts;  it  polarizes  rapidly  and  hence  is  best  suited 
for  open  circuit  work.  A  cross-section  of  a  dry  cell  is  shown 
in  Fig.  66. 

90.  Edison  Cell. — Another  single-fluid  cell  uses  for  the  posi- 
tive electrode  a  plate  of  copper  oxide,  zinc  for  the  negative 
electrode  and  a  solution  of  sodium  hydroxide  (caustic  soda) 
for  the  electrolyte.  The  top  of  the  electrolyte  is  covered  with 
a  heavy  oil  to  protect  the  zinc  from  attack  by  the  solution  of 
caustic  soda.  The  pressure  of  this  cell  ranges  from  0 . 5  to  about 
0.7  volt  on  closed  circuit.  The  internal  resistance  of  the  Edi- 


CURRENT  ELECTRICITY 


99 


son  cell  is  low  and  it  has  a  comparatively  high  current  capacity. 
It  is  suitable  for  either  open  or  closed  circuit  work.  A  form 
of  the  cell  is  shown  in  Fig.  67. 

91.  Two-fluid  Cells. — The  most  common  two-fluid  cell  is 
the  Daniell  cell  or  some  modified  form  of  it.  The  original 
form  of  the  Daniell  cell  is  shown  in  Fig.  68. 
As  shown  the  essential  parts  of  the  cell  are 
a  cylinder  of  copper  for  the  positive  electrode, 
a  rod  of  zinc  for  the  negative  electrode,  copper 
sulphate  and  zinc  sulphate  for  the  electrolyte, 
a  porous  cup  and  glass  jar  for  container.  The 
copper  electrode  is  immersed  in  a  saturated 
solution  of  copper  sulphate.  The  zinc  or  nega- 
tive electrode  is  placed  within  the  porous  cup 
and  is  surrounded  by  a  weak  solution  of  zinc 
sulphate.  The  purpose  of  the  porous  cup  is 
to  prevent  the  mixing  of  the  two  solutions.  When  the  cell 
is  first  set  up  the  solution  around  the  negative  electrode  is 
dilute  sulphuric  acid.  This  acid  acts  upon  the  zinc,  forming 
zinc  sulphate,  and  accordingly  the  solution  around  the  zinc 
grows  denser  with  use.  The  hydrogen  that  is  set  free  by  the 


FIG.  67. 


FIG.  68. 


action  of  the  acid  upon  the  zinc  passes  through  the  porous  cup 
and  combines  with  the  copper  sulphate  forming  sulphuric  acid 
and  copper.  The  copper  is  deposited  upon  the  copper  plate  or 
cylinder  and  hence  no  polarization  takes  place.  We  may 
thus  consider  the  copper  sulphate  as  a  depolarizer.  Since  the 


100  MAGNETISM  AND  ELECTRICITY 

copper  sulphate  is  constantly  being  decomposed  when  the  cell 
is  in  action,  the  copper  sulphate  solution  grows  weaker  with 
use.  An  excess  of  copper  sulphate  crystals  is  always  put  into 
the  solution  to  insure  continuous  action. 

92.  Gravity  Cell. — The  gravity  cell  is  merely  a  modification 
of  the  Daniell  cell.     In  the  gravity  cell  the  positive  electrode 
is  made  of  copper  and  is  placed  at  the  bottom  of  the  jar  as 
shown  in  Fig.  69.     Around  the  copper  is  placed  a  saturated 
solution   of   copper    sulphate.     Upon   the   copper    sulphate   is 

then  poured  dilute  sulphuric  acid 
within  which  is  placed  the  nega- 
tive electrode  made  of  zinc  cast 
in  the  shape  of  a  crow's  foot, 
whence  the  name  "  crowfoot  grav- 
ity cell."  The  two  solutions  are 
of  different  densities;  that  is,  zinc 
sulphate  is  lighter  than  the  copper 
-  sulphate,  and  hence  the  solutions 
do  not  mix  while  the  cell  is  in  ac- 
FIQ.  69.  tion.  If  the  cell  should  be  left 

open  circuited  for  some  time  the 

solutions  will  mix  and  will  have  to  be   renewed  and  the  zinc 

cleaned  and  amalgamated. 

The  electromotive  force  of  the  Daniell  cell  is  about  1.1  volts, 

and  as  it  does  not  polarize  it  is  used  very  extensively  on  closed 

circuit  work,  that  is,  on  circuits  that  require  a  continuous  flow 

of  current. 

93.  Experiment  24.    Electromotive  Force  of  Different  Cells. 
Apparatus. — 

Demonstration  cell  consisting  of  glass  cup,  porous  cup, 
zinc,  carbon,  copper,  lead,  iron,  aluminum,  tin,  and 
nickel  strips 

Porcelain  cap 

1  oz.  sulphuric  acid 

Few  crystals  copper  sulphate 

2  oz.  ammonium  chloride 
Volt-ammeter 
Connectors  and  wire 

Operation. — The  purpose  of  this  experiment  is  to  determine  the 
electromotive  force  of  cells  made  of  different  materials.  The 
student  has  already  determined  the  e.m.f.  of  the  simple  cell. 


CURRENT  ELECTRICITY 


101 


Exactly  in  the  same  way  set  up  a  simple  cell  and  measure  the 
electromotive  force  when  the  following  strips  are  used  in  pairs 
as  electrodes: 


Positive 

copper 

carbon 

lead 

aluminum 

nickel 

copper 

carbon 

carbon 

carbon 


Negative 

zinc 

zinc 

zinc 

zinc 

zinc 

lead 

lead 

aluminum 

nickel 


Be  careful  to  read  the  voltage  as  soon  as  the  circuit  is  closed. 
If  this  is  not  done,  polarization  will  set  in  and  the  readings  will 
be  too  low.  Tabulate  the  results  as  follows: 


Electrodes 

Electrolyte 

Voltage 

Positive 

Negative 

Copper, 
etc. 

Zinc, 
etc. 

Dilute  sulphuric 
acid, 
etc. 

0.85  volt, 
etc. 

Next  dissolve  the  ammonium  chloride,  commonly  called  sal- 
ammoniac,  in  about  three-fourths  of  a  tumbler  of  water.  For 
electrodes  use  carbon  and  zinc.  Having  set  up  the  cell  again, 
measure  its  voltage  as  above  described.  Keep  the  circuit  closed 
through  the  voltmeter  for  a  time  and  observe  the  effect  of 
polarization. 

The  foregoing  experiments  are  all  with  single-fluid  cells. 
One  more  experiment  may  be  performed  to  show  that  a  Daniell 
cell  does  not  polarize.  Dissolve  the  crystals  of  blue  vitriol 
(copper  sulphate)  in  one-half  a  tumbler  of  water.  Leave  this 
in  the  tumbler.  Fill  the  porous  cup  about  one-half  full  of 
pure  water  and  add  one-fourth  as  much  sulphuric  acid.  Place 
an  amalgamated  zinc  rod  within  the  porous  cup  for  the  negative 
electrode  and  a  copper  strip  in  the  solution  of  copper  sulphate 
for  the  positive  electrode.  Set  the  porous  cup  inside  of  the 
tumbler  and  connect  the  electrodes  to  the  voltmeter  and 


102 


MAGNETISM  AND  ELECTRICITY 


observe  the  deflection.  Keep  the  circuit  through  the  voltmeter 
closed  for  some  time  and  observe  if  the  deflection  decreases. 
Record  all  of  the  facts  observed. 

94.  Theory. — The  foregoing  experiments  show  that  the  pres- 
sure a  cell  develops  depends  upon  the  material  of  which  the 
cell  is  made.     The  size  of  the  plates  has  nothing  to  do  with  the 
value  of  the  electromotive  force  on  open  circuit.     The  size  of 
the  plates  will,  of  course,  determine  the  capacity  of  the  cell 
to  deliver  current,  but  not  the  pressure. 

The  experiments  also  show  the  single-fluid  cells,  such  as  the 
Leclanche  cell,  etc.,  polarize  rapidly,  and  that  the  Daniell  cell 
does  not  polarize.  The  reason  for  this  is  the  fact  that  as  a 
result  of  the  electro-chemical  action  within  the  cell,  copper  is 
deposited  upon  the  copper  electrode.  The  hydrogen 
combines  with  the  copper  sulphate,  producing  sulphuric 
acid  and  liberating  copper.  The  solution  around  the 
negative,  or  zinc,  electrode  gradually  increases  in 
density  while  that  around  the  positive  electrode  de- 
creases in  density.  This  is  the  reason  why  an  excess 
of  copper  sulphate  crystals  is  required  around  the 
copper  electrode. 

The  fact  that  the  Leclanche  cell,  and  others  like 
it,  polarizes  rapidly  makes  it  suitable  only  for  inter- 
mittent work,  that  is,  for  work  where  the  circuit  re- 
mains closed  for  only  a  brief  instant.  During  the  time 
that  the  circuit  is  opened  the  polarization  disappears 
and  the  cell  is  again  ready  for  use. 

The  Daniell  cell,  on  the  other  hand,  does  not  polarize 
and  accordingly  it  is  suitable  for  closed  circuit  work  such  as 
telegraphy. 

95.  Practical  Application  of  Cells. — There  are  so  many  opera- 
tions for  which  primary  cells  are  used  that  only  a  few  can  be  given. 
In  many  domestic  operations  such  as  the  ringing  of  door  bells, 
operation  of  dampers,  and  heat-regulating  devices,  some  form 
of  primary  cell  is  used  extensively.     In  the  operation  of  the  tele- 
phone and  telegraph,  and  in  the  operation  of  the  ignition  systems 
of  gas  and  gasoline  engines,  great  numbers  of  the  cells  are  used. 
Steam  railway  signal  systems  are  often  operated  by  the  Edison 
cells,  and  another  application  of  the  primary  cell  which  is  greatly 
on  the  increase  is  the  pocket  flash  lamp,  one  form  of  which  is 
shown  in  Fig.  70. 


FIG.  70. 


CURRENT  ELECTRICITY  103 

RECAPITULATION 

1.  A  primary  cell  is  a  combination  of  electrolyte,  electrodes,  and  con- 
tainer such  that  the  chemical  action  taking  place  between  electrodes 
and  electrolyte  is  the  primary  or  immediate  source  of  the  electric 
current. 

2.  By  amalgamation  is  meant  the  process  of  coating  zinc  with  mercury. 

3.  By  local  action  is  meant  the  destructive  action  of  electric  currents 
set  up  between  the  impurities  in  the  zinc  electrode  and  the  zinc 
itself.    Amalgamation  covers  these  impurities  with  mercury  and  thus 
decreases  these  currents. 

4.  A  conductor  is  a  material  along  or  through  which  a  current  of  electric- 
ity can  be  transferred. 

5.  The  electromotive  force  or  electrical  pressure  of  a  cell  is  the  cause  of 
the  flow  of  an  electric  current  when  the  circuit  is  closed.    It  is  analo- 
gous to  water  pressure. 

6.  The  pressure  a  cell  develops  depends  upon  the  material  of  which  it 
is  made. 

7.  The  unit  of  electrical  pressure  is  the  volt.    The  volt  is  equal   to 
l^rrf  f§-  of  the  pressure  of  the  Weston  standard  cell  at  20  degrees 
centigrade. 

8.  Polarization  is  the  decrease  in  the  resultant  pressure  of  a  cell.     It  is 
caused  by  the  hydrogen  and  the  positive  electrode. 


CHAPTER  VI 
ELECTROLYSIS 

96.  Introduction. — The  word  electrolysis  in  ordinary  language 
is  used  in  two  senses.     One  use  of  the  word  has  reference  to  the 
corrosive  action  of  the  electric  current  on  underground  or  imbed- 
ded iron  pipes  or  rods.     The  second  use  of  the  word  has  reference 
to  the  decomposition  of  liquids  by  the  passage  of  an  electric 
current.     This  is  the  meaning  of  electrolysis  as  used  in  the  follow- 
ing discussion. 

97.  Liquid   Conductors. — With  reference   to   the  manner   in 
which  liquids  conduct  electricity  they  can  be  divided  into  three 
classes : 

1.  Insulators. — In    some    cases     liquids    offer    a    very    high 
resistance  to  the  flow  of  current  and  act  as  insulators.     Such  is 
the  case  with  paraffin  oil,  turpentine,  etc. 

2.  Conductors. — Some  liquids,  like  mercury  and  molten  metals, 
conduct  electricity   in  the  same  manner  as  solid   conductors. 
When  electricity  is  passed  through  these,  no  decomposition  or 
chemical  action  takes  place. 

3.  Electrolytes. — Solutions  of   acids,   bases,    or   salts   conduct 
electricity  by  undergoing  decomposition,  when  electric  current 
is  passed  through  them.     Such  solutions  are  called  electrolytes. 

98.  Experiment  25.    Electrolytic  Decomposition. 
Apparatus. — 

Two  dry  cells 

Tumbler 

A  little  sulphuric  acid 

Some  copper  sulphate  crystals 

Operation. — Take  a  tumbler  and  fill  it  about  half  full  with  pure 
water.  Connect  the  two  dry  cells  in  series,  that  is,  connect  the 
carbon  rod  in  the  center  of  one  cell  with  the  zinc  cup  of  the  other 
cell.  To  the  two  remaining  terminals  connect  two  copper  wires 
about  1  ft.  long  each.  Dip  the  exposed  ends  of  the  copper  wires 
into  the  water  in  the  tumbler,  keeping  them  about  1  in.  apart 
as  indicated,  in  Fig.  71.  Do  any  gas  bubbles  rise  from  either 
wire?  To  which  class  of  liquids  does  pure  water  belong? 
11  105 


106 


MAGNETISM  AND  ELECTRICITY 


Carefully  pour  about  a  thimbleful  of  sulphuric  acid  into  the 
tumbler  of  water.  Stir  the  mixture  with  a  stick,  then  again 
dip  the  two  exposed  ends  of  the  wires  into  the  liquid.  Does  any 
gas  rise  from  the  wires?  To  be  sure  that  the  gas  is  not  due  to 
chemical  action  between  acid  and  copper  wires,  take  two  wires 

that  are  not  connected  to  the 
dry  batteries  and  dip  them 
into  the  solution.  Is  the  ac- 
tion the  same  as  when  wires 
connected  to  the  cell  were 
dipped  into  the  liquid?  Re- 
peat the  experiment  again  and 
see  at  which  wire  most  gas  col- 
lects. Is  it  the  wire  connected 
to  the  carbon  or  zinc  electrode 
FIG.  71.  of  the  cells? 

When   you   have   satisfied 

yourself  on  this  point,  throw  the  acid  solution  away.  Dissolve 
a  large  crystal  or  two  of  copper  sulphate  in  about  half  a  tumbler 
of  water.  Wrap  the  end  of  the  wire  that  is  connected  to  the 
negative  electrode  around  one  end  of  a  nail,  or  use  one  of  the 
connectors  for  making  this  connection.  Dip  the  nail  and  the 
other  wire  into  the  solution  of  copper  sulphate  as  indicated  in 
Fig.  72.  After  ten  or  fifteen 
minutes,  withdraw  the  nail 
and  examine  it.  Has  it 
changed  color?  Is  it  coated 
with  rust  or  copper?  Where 
did  the  coating  come  from? 
Connect  the  nail  to  the  other 
electrode  of  the  dry  cells  and 
again  immerse  it  in  the  solu- 
tion as  before.  Leave  it  there 
for  about  15  minutes  and  then 
examine  again.  Does  it  still 
have  the  dull  red  coating? 
What  has  become  of  it? 

Connect  one  nail  to  each  electrode  and  dip  both  of  them  into 
the  solution.  After  about  15  minutes  withdraw  both  and  examine 
them.  Are  they  both  coated?  To  which  terminal  of  the  cell 
is  the  coated  one  connected?  Does  gas  escape  from  the  elec- 


FIG.  72. 


ELECTROLYSIS  107 

trolytic  cell?     The  tumbler,  solution  and  electrodes,  in  this  case 
nails,  are  called  an  electrolytic  cell. 

To  which  class  of  liquids  do  solutions  of  sulphuric  acid  and 
copper  sulphate  belong? 

99.  Theory. — If  the  student  has  carefully  performed  the  fore- 
going experiment,  he  has  learned  that  pure  water  is  practically 
a  non-conductor,  but  when  a  solution  of  sulphuric  acid  is  made 
it  becomes  a  fairly  good  conductor.     The  transfer  of  electricity 
through  the  solution  is  explained  on  the  supposition  that  in  the 
process  of  solution  the  sulphuric  acid  is  dissociated.     This  will 
be  explained  more  fully  later. 

100.  Anode  and  Cathode. — The  terminal  by  which  a  current 
enters  the  electrolytic  cell  is  calfed  the  anode,  and  the  terminal 
by  which  the  current  leaves  the  cell  is  called  the  cathode.     The 
solution  is  the  electrolyte  as  explained  in  the  preceding  chapter. 

The  student  observed  that  when  the  current  is  passed  through 
the  solution  of  sulphuric  acid,  gas  collects  at  each  terminal,  but 
that  more  accumulates  at  the  cathode  than  at  the  anode  The 
gas  that  collects  at  the  anode  is  oxygen  and  the  gas  collecting  at 
the  cathode  is  hydrogen.  In  the  same  way  when  current  is 
passed  through  the  copper  sulphate  solution,  copper  is  deposited 
at  the  cathode  while  the  anode  remains  clean.  It  is  thus  seen 
that  some  substances  travel  with  the  current  while  others  move 
against  the  current. 

101.  Dissociation  Theory. — Within  recent  years  a  theory  has 
been  advanced  to  explain  the  action  of  an  electrolytic  cell. 
While  this  theory  has  not  been  proved  in  all  its  phases,  neverthe- 
less, it  is  helpful  in  giving  an  understanding  of  electrolysis  and 
electrolytic  processes.     The  elements  of  the  theory  are  as  follows : 
In  the  preceding  experiment  the  student  learned  that  pure  water 
is  practically  a  non-conductor.     The  same  is  true  of  pure  sul- 
phuric acid;  nevertheless  a  mixture  of  the  two  conducts  electricity 
fairly  well.     Sulphuric  acid  is  a  compound  consisting  of  hydrogen 
(H),  oxygen  (0),  and  sulphur  (S).     The  chemical  symbol  for  it 
is  H2S04.     According  to  the  dissociation  theory  where  sulphuric 
acid  is  dissolved  in  water  the  sulphuric  acid  is  decomposed  or 
dissociated  into  two  groups  of  atoms.     One  group  (H2)  is  charged 
positively  and  the  other  group   (S04)   is  charged  negatively. 
These  charged  groups  of  atoms   are  called  ions.     When  the 
solution  is  subjected  to  an  electrical  pressure,  the  hydrogen  ions 
move  from  higher  to  lower  pressure;  that  is,  toward  the  cathode 


108  MAGNETISM  AND  ELECTRICITY 

where  they  deposit  their  charge  and  escape  as  pure  hydrogen 
atoms.  The  sulphions  (S04)  move  against  the  current  and  at 
the  anode  they  deposit  the  negative  charge.  When  freed  from 
the  negative  charge,  they  attack  the  water,  combining  with  the 
hydrogen,  while  oxygen  is  set  free. 

102.  Faraday's  Law. — We  have  just  learned  that  when  elec- 
tricity is  passed  through  a  salt  solution,  the  metal  of  the  salt  is 
deposited  upon  the  cathode.  After  many  exhaustive  experi- 
ments Faraday  formulated  two  laws  which  express  the  relation 
between  the  quantity  of  electricity  passing  and  the  mass  or  weight 
of  metal  deposited.  These  relations  are  known  as  Faraday's 
Laws,  and  are  as  follows: 

1.  When  electricity  is  passeol  through  a  solution,  the  mass  of 
the   decomposed   solution  is  proportional   to   the  quantity   of 
electricity  passing. 

2.  The  mass  of  any  substance  liberated  by  a  given  quantity 
of  electricity  is  proportional  to  the  chemical  equivalent  of  the 
substance. 

The  first  law  means  that  a  given  current  of  electricity,  flowing 
for  a  given  time,  will  always  deposit  the  same  mass  or  weight  of 
a  given  element  from  a  solution,  irrespective  of  the  concentration 
of  the  solution  that  contains  the  element  or  of  other  conditions. 

According  to  the  second  law,  the  mass  of  the  substance  de- 
posited will  depend  upon  its  combining  weight,  which  is  called 
chemical  equivalent.  Thus,  when  a  solution  of  copper  salt  is  used 
as  the  electrolyte,  the  mass  of  copper  deposited  will  depend  on 
whether  a  cupric  or  cuprous  salt  is  used.  The  chemical  symbol  for 
cupric  chloride  is  CuC^  and  for  cuprous  chloride  CuCl.  From 
this  it  will  be  seen  that  two  atoms  of  copper  in  the  cuprous 
compound  take  the  place  of  one  atom  in  the  cupric  compound. 
The  combining  weight  is  twice  as  great,  and  twice  as  much  copper 
will  be  deposited  by  a  given  current  from  a  cuprous  solution  as 
from  the  cupric  solution.  The  law  also  states  that  if  solutions 
of  different  compounds  be  decomposed,  the  weight  of  material 
deposited  by  a  given  current  is  proportional  to  the  combining 
weight  of  the  materials  or  elements  forming  the  compounds. 
Thus,  1  ampere  sent  through  a  solution  of  silver  nitrate  for 
an  hour  will  deposit  4.025  grm.  of  silver.  The  same  current  sent 
through  a  solution  of  copper  sulphate  will  deposit  only  1.184 
grm.  of  copper  in  one  hour.  These  laws  are  the  fundamental 
principles  of  the  operation  of  electro-chemical  measuring  instru- 


ELECTROLYSIS  109 

ments.     The  electro-chemical  equivalents  of  some  metals  are 
given  in  the  following  table: 


TABLE  IV 

Metal 

Electro-chemical  equivalent  in 
per  coulomb 

milligrams 

Aluminium  
Copper 

0.0936 
0  6588 

Copper 

0  3290 

Gold  
Iron 

0.6818 
0  2894 

Iron 

0  1929 

Lead  
Nickel 

1.0731 
0  3040 

Silver 

1  1180 

Zinc  

0.3385 

It  is  noticed  that  two  values  are  given  in  the  table  for  copper 
and  iron.  This  is  because  each  of  these  has  different  combining 
powers,  as  explained  above.  The  value  0.3290  for  copper  usually 
applies  when  copper  is  deposited  in  an  electrolytic  cell.  The 
table  may  be  reduced  to  English  units  by  remembering  that  1 
grm.  is  equal  to  0.0353  oz.,  avoirdupois. 

103.  Electric  Current. — We  have  already  used  the  words 
electric  current  several  times  without  explanation.  Perhaps  an 
explanation  will  not  greatly  aid  in  giving  an  understanding  of 
the  physical  phenomena,  nevertheless  it  will  be  attempted. 

The  transfer  of  electrical  energy  along  wires  or  conductors  is 
in  many  respects  like  the  transfer  of  energy  by  water  when 
flowing  through  pipes.  For  this  reason  many  words  that  are 
used  in  describing  the  flow  of  water  are  used  when  the  transfer 
of  energy  by  electrical  means  is  considered. 

When  water  flows  through  pipes,  the  energy  transferred  by 
it  in  a  given  time  depends  upon  the  current  and  head  or  pressure. 
The  current  is  defined  as  the  number  of  cubic  feet  or  gallons  of 
water  flowing  past  any  point  in  a  second  or  some  other  unit  of 
time.  The  current  is  then  the  rate  of  flow  of  water. 

Electrical  energy  may  be  transferred  along  or  by  means  of  a 
conductor.  The  transfer  of  energy  is  said  to  be  by  means  of 
a  current  of  electricity.  Thus  the  rate  of  flow  of  electricity  is 
also  called  a  current.  An  electric  current  may  then  be  defined 
as  a  continuous  transference  of  electrical  energy  from  its  source 
to  other  parts  of  the  circuit. 


110  MAGNETISM  AND  ELECTRICITY 

In  measuring  a  water  current  it  is  possible  to  measure  the 
quantity  of  water  discharged  and  thus  the  rate  of  flow  can  be 
determined  by  dividing  the  total  quantity  by  the  time  of  flow. 
It  is  not  practical  to  measure  an  electric  current  in  this  way. 
The  electric  current  is  measured  by  means  of  its  electrolytic, 
magnetic,  or  heat  effects.  The  unit  current  has  been  defined  in 
accordance  with  Faraday's  first  law. 

104.  Definitions. — The    ampere    is    the    unvarying    electric 
current  which,   when  passed  through  a   standard  solution  of 
silver  nitrate,  deposits  silver  at  the  rate  of  0.001118  grm.  per 
second.     An  ampere  will  thus  deposit  4.025  grm.  of  silver  per 
hour. 

Coulomb. — The  coulomb  is  the  unit  quantity  of  electricity 
and  is  the  quantity  of  electricity  given  by  one  ampere  in  one 
second.  Thus  according  to  the  definition  of  ampere  given 
above,  when  one  coulomb  of  electricity  is  passed  through  a 
standard  solution  of  silver  nitrate,  0.001118  grm.  of  silver  are 
deposited  upon  the  cathode. 

Electro-chemical  Equivalent. — The  mass  of  any  metal  de- 
posited by  one  coulomb  of  electricity  is  called  the  electro-chemical 
equivalent.  Thus  in  the  table  on  page  109  the  electro-chemical 
equivalents  are  given  in  milligrams.  One  milligram  equals 
0.001  grm. 

EXAMPLES 

1.  How  many  grams  of  copper  will  be  deposited  by  100,000  coulombs  of 
electricity? 

Solution. — 1  coulomb  deposits  0.000329  grm.    100,000  coulombs  will 
deposit  100,000X0.000329=32.9  grm. 

2.  A  steady  current  is  passed  for  one  hour  through  a  silver  nitrate  solution. 
If  13.68  grm.  of  silver  are  deposited,  what  is  the  current? 

Solution. — In  one  hour  1  ampere  deposits  4.025  grm.     Hence  current 
required  to  deposit  43.68  grm.  is  43.68-^4.025  =  10.85  amperes. 

105.  Secondary   or   Storage    Cells. — The   principle   of   elec- 
trolysis is  applied  in  producing  a  chemical  change  which  under 
proper  conditions  is  reversed  and  the  chemical  energy  is  con- 
verted into  electrical  energy  or  energy  of  the  electrical  current. 
Electrolytic  cells  which  are  used  for  this  purpose  are  called 
secondary    or   storage    cells.     The    essential   principles    will    be 
made  clear  by  the  following  experiment. 


ELECTROLYSIS 


111 


106.  Experiment  26.     Principles  of  the  Storage  Battery. 

Apparatus. — 

Two  1  in.  X  6  in.  strips  of  lead 

Tumbler 

Dilute  sulphuric  acid 

Ammeter 

Electric  bell 

Operation. — Fasten  the  two  lead  strips  on  opposite  sides  of  a 
dry  piece  of  wood  ?X1X4  in.  Between  each  lead  strip  and 
the  wood  clamp  a  piece  of  copper  wire  for  connections,  or  drill 
a  hole  in  each  strip  and  fasten  a  wire  in  it.  The  holder  of  the 
experimental  cell  may  be  used  in  place  of  the  block  of  wood. 


FIG.  73. 

Immerse  the  two  lead  strips  in  a  solution  consisting  of  one  part 
of  sulphuric  acid  to  ten  parts  of  rain  water.  Connect  three  dry 
cells  in  series  and  then  arrange  the  apparatus  as  shown  in  Fig. 
73.  Close  switch  K\  and  leave  K%  open.  As  the  current  flows, 
bubbles  will  be  seen  to  arise  from  the  cathode,  while  the  anode 
will  begin  to  turn  a  dark  brown.  Observe  carefully  the  behavior 
of  the  ammeter.  After  about  twenty  minutes  open  key  K\ 
and  close  Kz-  Does  the  bell  ring?  Observe  the  deflection 
of  the  ammeter.  Is  it  in  the  same  direction  as  before  or  in  the 
opposite  direction?  Reverse  the  switch  S  and  observe  how 
rapidly  the  current  decreases. 

107.  Theory. — This  experiment  illustrates  the  principles   of 
the  storage  cell.     The  student  observed  that  the  color  of  the 


112  MAGNETISM  AND  ELECTRICITY 

anode  changes  from  the  natural  color  of  lead  to  brown.  This 
brown  coating  is  a  compound  of  lead  and  oxygen,  called  lead 
peroxide  with  a  chemical  symbol  (Pb02).  This  lead  peroxide 
is  formed  by  the  action  upon  the  plate  of  the  oxygen.  When 
the  charging  circuit  is  opened  and  the  circuit  through  the  bell 
is  closed,  the  cell  acts  exactly  like  a  primary  cell  and  furnishes 
a  current  until  all  of  the  peroxide  is  used  up.  This  current  is 
due  to  the  conversion  of  the  lead  peroxide  into  metallic  lead. 
This  is  also  a  chemical  change.  Properly  speaking,  there  has 
been  no  storage  of  electricity  but  only  a  storage  of  energy. 
In  other  words,  the  energy  of  the  current  which  is  sent  into  the 
cell  is  expended  in  producing  chemical  changes  upon  the  elec- 
trodes, and  therefore,  it  remains  as  potential  energy  until  a 


FIG.  74.  FIG.  75. 

wire  connects  the  two  plates,  when  it  again  appears  as  the 
energy  of  the  electric  current.  In  a  good  storage  cell  the  energy 
that  has  been  expended  in  charging  may  remain  for  weeks  as 
potential  energy  without  serious  loss. 

In  addition  to  the  simple  reaction  described  there  are  other 
reactions  or  changes  taking  place  both  on  charging  and  dis- 
charging. Some  of  these  are  not  very  well  understood  and  the 
one  mentioned  is  undoubtedly  the  one  to  which  the  action  of 
the  storage  cell  is  principally  due. 

108.  The  Lead  Storage  Cell. — The  only  important  difference 
between  the  lead  commercial  storage  cell  and  the  experimental 
one  used  is  that  the  commercial  cell  is  provided  in  the  making 
with  a  much  thicker  coat  of  the  lead  peroxide  on  the  positive 
plate,  Fig.  74,  and  of  the  spongy  lead,  lead  oxide  (PbO)  on  the 


ELECTROLYSIS 


113 


negative  plate,  Fig.  75.  This  material  is  pressed  into  the 
interstices  in  the  plates.  A  complete  lead  storage  cell  also 
called  accumulator,  is  shown  in  Fig.  76. 

The  lead  plates  have  little  rigidity  and  easily  become  warped. 
If  discharged  or  charged  too  rapidly,  the  plates  become  hot 
and  buckle,  that  is  twist  out  of  shape,  thus  short  circuiting 
the  cell  and  destroying  its  usefulness.  If  the  cell  is  allowed 
to  stand  discharged  for  a  few  weeks,  the  lead  sulphate  formed 


FIG.  76. 

on  the  negative  plate  during  discharge  becomes  hard;  this 
interferes  with  the  proper  working  of  the  cell.  Unless  storage 
cells  are  watched  and  kept  in  good  condition,  they  deteriorate 
rapidly  and  quickly  get  out  of  order.  All  contacts  and  metal 
parts  near  the  cell  must  be  lead  covered  to  protect  them  from 
the  action  of  the  sulphuric  acid.  For  permanent  installations 
the  containers  are  of  glass,  but  where  the  cell  is  to  be  portable 
the  container  is  usually  a  rubber  jar,  Fig.  77.  The  efficiency 


114 


MAGNETISM  AND  ELECTRICITY 


of  the  lead  cell  is  about  75  per  cent;  that  is,  only  about  three- 
fourths  of  the  energy  used  on  charging  can  be  obtained  for  useful 

work  on  discharging. 

The  voltage  of  the  lead 
storage  cell  depends  upon 
the  character  of  the  elec- 
trodes and  the  density  of 
the  electrolyte.  On  charge 
and  discharge  the  voltage  of 
the  lead  storage  cell  changes 
as  represented  by  curves, 
Fig.  78.  The  voltage 
should  never  be  allowed  to 
drop  below  1.7  volts,  for  if 
it  does  it  will  become  so 
badly  sulphated  that  it  will 
FlG-  77«  be  practically  impossible  to 

restore  the  cell  to  normal  condition. 

109.  The  Nickel-Iron   Cell.— The  lead  storage   battery  has 
several  disadvantages  in  practical  use.     Among  the  most  promi- 


2.4 


£.0 


/.a 


FIG.  78. 


nent  may  be  mentioned  the  following:  the  giving  off  of  acid 
fumes  which  makes  necessary  special  construction  of  rooms  for 


ELECTROLYSIS 


115 


116 


MAGNETISM  AND  ELECTRICITY 


...... ..t  , . 


FIG.  79. 


FIG.  79a. 


housing  the  battery  and  also  necessitates  extra  ventilation;  the 

rapid  deterioration  of  the  plates; 
excessive  weight  when  used  for  au- 
tomobiles, etc.  Many  attempts 
have  been  made  to  either  remove 
these  objectionable  features,  or  to 
discover  some  substances  out  of 
which  a  cell  could  be  made  which 
will  not  inherently  possess  these 
disadvantages.  The  storage  cell 
invented  and  designed  by  Mr. 
Thomas  A.  Edison  is  free  from  some 
of  the  foregoing  defects.  The  con- 
tainer of  the  Edison  storage  cell  is 
a  jar  of  nickel-plated  steel  which  is 
not  readily  broken.  The  electrodes 
are  of  iron  and  nickel  and  the  elec- 
trolyte is  a  solution  of  caustic 
potash. 
FIG.  80.  The  negative  plate,  Fig.  79,  con- 


ELECTROLYSIS 


117 


sists  of  a  gridiron  of  steel  with  a  paste  of  iron  oxide  in  the  pockets. 
The  pockets  are  made  of  thin  nickel-plated  steel,  perforated 
with  fine  holes.  The  positive  plate,  Fig.  80,  is  a 
framework  of  steel  within  which  are  some  thirty 
steel  tubes  about  the  size  of  lead  pencils,  Fig.  80a. 
These  tubes  are  perforated  and  contain  alternate 
layers  of  nickel  oxide  and  nickel,  the  nickel  serving 

the  purpose  of  a  conductor. 
In  a  cell  the  positive 
and  negative  plates  are  as- 
sembled alternately,  the 
positive  plates  are  all  con- 
nected together  and  like- 
wise the  negative  plates 
are  connected  together  in 
order  to  increase  the  ca- 
pacity of  the  cell.  The 
complete  cell  is  shown  in 
Fig.  81. 

The  advantages  of  the 
nickel-iron  cell  are  its  me- 
chanical strength,  weak  or 
comparatively  harmless 
electrolyte,  and  relatively 
high  output  per  pound  of 
cell.  The  voltage  of  the 


FIG.  80a. 


cell  is  only  about  one-half  as  high  as 
that  of  the  lead  cell,  and  its  efficiency 
is  only  about  60  per  cent,  when  charged 
and  discharged  in  accordance  with  the 
curves  shown  in  Fig.  82. 

110.  Electroplating. — The  fact  that 
the  solution  of  a  metal  salt  is  decom- 
posed by  the  passage  of  an  electric 
current  through  it  has  made  possible 
the  process  of  plating  or  coating  the 
baser  metals  with  copper,  gold,  silver, 
nickel,  etc.  The  process  in  general  con- 
sists in  immersing  the  body  to  be  plated 

in  a  solution  of  a  salt  of  the  metal  with  which  the  body  is  to  be 
plated.     The  anode  is  nearly  always  made  of  the  same  substance 


118 


MAGNETISM  AND  ELECTRICITY 


as  that  to  be  deposited  from  the  solution.  The  body  to  be  plated 
is  always  the  cathode.  For  detailed  descriptions  the  student 
is  referred  to  handbooks  on  electroplating. 

111.  Voltages  for  Electroplating. — Experiments  show  that  the 
most  suitable  voltages  for  electroplating  are  about  as  follows: 

TABLE  V 

Copper  in  sulphate 1 . 5  to  2 . 5  volts 

Copper  in  cyanide 4 . 0  to  6 . 0  volts 

Silver  in  cyanide 1 . 0  to  2 . 0  volts 

Gold  in  cyanide 0. 5  to  3 .0  volts 

Nickel  in  sulphate 2 . 5  to  5 . 5  volts 

112.  Critical  Current  Density. — From  theoretical  considera- 
tions one  might  conclude  that  the  higher  the  current  the  more 


FIG.  82. 

rapidly  would  the  process  of  electroplating  proceed.  It  is  true 
that  the  decomposition  of  the  solution  would  proceed  at  a  higher 
rate  the  higher  the  current  density,  but  practical  difficulties 
are  encountered  if  the  current  density  is  too  high,  or  above  a 
certain  value  called  the  critical  current  density.  A  current 
greater  than  the  critical  value  results  in  depositing  the  hydrogen 
in  conjunction  with  the  metal,  and,  as  a  consequence,  the  depos- 
ited metal  will  not  adhere  and  make  a  smooth  coating.  By 
rotating  the  cathode  a  much  higher  current  density  may  be  used 
and  still  obtain  good  results. 

113.  Electrotyping. — In  the  process  of  making  plates  for  print- 
ing by  electrolytic  deposition,  the  page  is  first  set  up  in  common 


ELECTROLYSIS 


119 


type.  An  impression  is  then  made  in  wax.  This  mold  is  then 
coated  with  powdered  graphite  to  make  it  a  conductor,  after 
which  it  is  ready  to  be  suspended  as  the  cathode  in  a  copper 
plating  bath,  the  anode  being  a  copper  plate  and  the  electrolyte 
a  solution  of  copper  sulphate.  When  a  film  of  the  desired  thick- 
ness has  been  formed,  the  mold  is  removed  by  pouring  hot  water 
on  it,  after  which  the  film  is  backed  by  the  type  metal  to  give 
it  the  necessary  rigidity.  A  good  copper  plating  bath  can  be 
made  as  follows: 

Dissolve  about  20  grm.  of  copper  acetate  in  500  c.c.  (a  little 
over  one  pint)  of  water.  Dissolve  20  grm.  potassium  cyanide, 
25  grm.  sodium  sulphate  crystals,  and  17  grm.  of  sodium  carbon- 
ate crystals  in  another  500  c.c.  of  water.  Then  add  the  first 
solution  to  the  second  one.  For  plating,  a  current  density  of 


lb  dynamo 


Anodes 


Cathodes- 


Cathodes 


FIG.  83. 

0.003  ampere  per  square  centimeter  is  then  used  with  3  volts 
at  the  terminals  of  the  cell. 

114.  Gold  and  Silver  Plating. — Gold  and  silver  plating  are 
carried  on  in  much  the  same  manner.     Three  solutions  are  used 
in  gold  plating  to  give  the  different  coloring  effects  known  as 
California,  green  and  red  gold.     In  making  the  solutions  the 
following  salts  are  dissolved  in  a  mixture  of  nitric  and  hydro- 
chloric acid. 

An  alloy  of  22  parts  gold  and  2  parts  silver  is  used  for  California 
gold;  an  alloy  of  16  parts  gold  and  8  parts  silver  is  used  for  green 
gold;  and  an  alloy  of  16  parts  gold  and  8  parts  of  copper  for  red 
gold.  The  anodes  are  of  pure  gold,  and  a  difference  of  electrical 
pressure  of  5  volts  is  maintained  across  them. 

115.  Refining    of    Metals.— Another    important   electrolytic 
process  is   the  process  of  refining  copper.     Fig.  83  shows  the 


120 


MAGNETISM  AND  ELECTRICITY 


arrangement  of  a  tank  or  bath  for  this  purpose.  The  copper 
to  be  refined  is  suspended  in  a  copper  sulphate  solution  and  cur- 
rent is  sent  through  them  to  the  cathodes.  As  the  anodes  of 
copper  are  eaten  away  the  impurities  fall  as  residue  to  the  bottom 
of  the  tank  and  pure  copper  is  deposited  on  the  cathode.  Other 
metals  can  also  be  refined  in  the  same  way. 

116.  Some  Other  Electrolytic  Processes. — When  electrical 
energy  is  comparatively  cheap,  as  at  Niagara  Falls  and  other 
water  powers,  various  electrolytic  processes  are  carried  on. 

Caustic  soda,  metallic  sodium,  alu- 
minum, potassium  chlorate,  and 
many  other  substances  are  manu- 
factured on  a  large  scale  by  modified 
electrolytic  processes.  Recently 
there  has  been  developed  and  placed 
on  the  market  an  apparatus  for  the 
purification  of  air  in  class-rooms, 
churches,  and  other  buildings. 
This  apparatus  generates  ozone  by 
an  electrical  discharge  in  the  air. 
The  ozone  then  acts  chemically  on 
the  impurities  reducing  them  to  a 
harmless  condition.  It  is  claimed 
that  the  ozonator,  as  the  apparatus 
is  called,  greatly  improves  the  sani- 
tary conditions  wherever  indoor  air  is  breathed.  The  appearance 
of  one  form  of  ozonator  is  shown  in  Fig.  84.  For  more  detailed 
explanations  of  electrolytic  processes  the  student  is  referred 
to  books  on  electro-chemistry: 


FIG.  84. 


RECAPITULATION 

1.  By  electrolysis  is  meant  the  process  of  chemical  decomposition  by 
the  passage  of  the  electrical  current. 

2.  According  to  their  electrical  properties  liquids  may  be  divided  into 
three  classes,  insulators,  conductors,  and  electrolytes. 

(a)  Liquids  act  as  insulators  when  they  offer  very  high  resistance 
to  the  flow  of  electricity. 

(b)  Liquids  act  as  conductors  when  their  conductivity  is  like  that 
of  solid  conductors. 

(c)  Liquids  are  called  electrolytes  when  they  suffer  decomposition 
by  the  passage  of  an  electric  current  through  them. 


ELECTROLYSIS  121 

3.  An  electrolytic  cell  is  a  combination  of  container,  electrolyte  and 
electrodes. 

(a)  The  anode  of  an  electrolytic  cell  is  the  electrode  by  which  current 
enters  the  cell. 

(b)  The  cathode  is  the  electrode  by  which  the  current  leaves  the 
electrolytic  cell. 

4.  Faraday's  laws  of  electrolysis  express  the  relation  between  the  mass 
of  the  electrolyte  decomposed  and  the  quantity  of  electricity  caus- 
ing the  decomposition.     They  are: 

(a)  When  electricity  is  passed  through  a  solution,  the  mass  of  the 
solution  decomposed  is  proportional  to  the  quantity  of  electricity 
passing. 

(b)  The  mass  of  any  substance  liberated  by  a  given  quantity  of 
electricity  is  proportional  to  the  chemical  equivalent  of  the  substance. 

5.  An  electric  current  is  the  name  given  to  a  continuous  transference 
of  electrical  energy  from  its  source  to  other  parts  of  the  circuit. 

(a)  The  practical  unit  of  electrical  current  is  the  ampere  and  is 
denned  as  that  current  which,  when  passed  through  a  standard 
solution  of  silver  nitrate,  deposits  silver  at  the  rate  of  0.001118 
grm.  per  second.  An  ampere  will  thus  deposit  4 . 025  grm.  ( =  0 . 1408 
oz.,  avoirdupois)  per  hour. 

6.  The  coulomb  is  the  unit  quantity  of  electricity,  and  is  the  quantity 
of  electricity  given  by  1  ampere  in  one  second. 

7.  By  electro-chemical  equivalent  is  meant  the  mass  of  any  metal  deposited 
by  one  coulomb  of  electricity. 


12 


CHAPTER  VII 
RESISTANCE 

117.  Introduction. — So  far  we  have  discussed  the  generation 
of  an  electromotive  force  both  by  chemical  and  mechanical 
means.     It  has  also  been  stated  that  when  a  source  of  electro- 
motive force  is  connected  to  a  circuit,  and  the  circuit  is  closed, 
an  electric  current  will  flow.     Nothing,  however,  has  been  said 
concerning  the  relation  between  the  strength  of  the  current,  the 
electromotive  force,  and  other  quantities  of  the  circuit. 

We  shall  now  investigate  and  determine  some  of  these  rela- 
tions. In  order  to  do  this  we  must  discuss  another  quantity 
which  plays  an  important  part  in  determining  the  flow  of  current 
in  a  circuit  but  which  so  far  has  been  barely  mentioned. 

118.  Electrical  Resistance. — A   clear   understanding   of  this 
quantity  will  be  perhaps  best  obtained  by  comparing  the  re- 
sistance a  conductor  offers  to  the  flow  of  an  electrical  current 
with  the  resistance  offered  by  a  pipe  to  the  flow  of  water  in  that 
pipe. 

If  the  pipe  be  connected  to  a  tank  in  which  the  water  is  kept 
at  a  constant  level,  a  definite  quantity  of  water  will  flow  through 
it  in  unit  time.  This  quantity  will  remain  constant  so  long  as 
the  height  of  the  water  in  the  tank  remains  constant.  The 
pressure  exerted  at  the  pipe  is  constant  and  the  current  is 
constant.  If,  however,  a  pipe  of  the  same  length  but  of  larger 
diameter  be  connected  to  the  same  place  on  the  tank,  a  greater 
current  will  flow.  This  is  explained  by  saying  that  the  larger 
pipe  offers  less  resistance  to  the  flow  of  water. 

Again,  if  a  short  pipe  be  replaced  by  a  long  one  of  the  same 
diameter  the  current  will  be  less;  that  is,  a  smaller  quantity  will 
flow  through  the  pipe  in  unit  time.  This  is  explained  by  saying 
that  a  long  pipe  has  a  greater  resistance  than  a  short  one  of  the 
same  diameter. 

If  we  replace  an  iron  pipe  with  a  smooth  inner  surface  by  a 
wooden  one  with  a  rough  inner  surface,  the  current  in  the  wooden 
one  will  be  less  even  though  the  diameters  of  the  two  pipes  are 
13  123 


124 


MAGNETISM  AND  ELECTRICITY 


equal.  In  this  case  the  materials  of  which  the  pipes  are  made 
are  different,  and  the  one  with  rough  inner  surface,  or  the  one  of 
wood,  offers  the  higher  resistance.  Summarizing  these  facts 
with  reference  to  water  pipes  we  find: 

1.  A  large  pipe  offers  less  resistance  to  the  flow  of  water 
than  a  small  one  of  the  same  length.     In  other  words,  the  same 
pressure  will  force  a  greater  current  through  a  large  pipe  than 
through  a  small  one. 

2.  A  long  pipe  offers  greater  resistance  to  the  flow  of  water 
than  a  short  one  of  the  same  diameter.     In  other  words  the 
same  pressure  will  force  a  larger  current  through  a  short  pipe 
than  through  a  long  one. 


FIG.  85. 

3.  The  resistance  offered  by  two  pipes  of  equal  lengths  and 
diameters  depends  upon  the  character  of  their  inner  surfaces; 
that  is,  upon  the  material  of  which  the  pipes  are  made. 

Whether  or  not  these  same  relations  hold  in  an  electrical 
circuit  we  shall  now  investigate. 

119.  Experiment  27.    To  Determine  Relation  between  Cur- 
rent and  Length  of  Conductor  When  Pressure  is  Kept  Constant. 
Apparatus. — 

Volt-ammeter 
Resistance  board 
Two  dry  cells 

Operation. — A  diagram  of  the  resistance  board  to  be  used 
in  this  experiment  is  shown  in  Fig.  85.  As  there  shown  this 
board  consists  of  four  coils — 1,  2,  3,  and  4 — mounted  in  such  a 


RESISTANCE 


125 


way  that  they  can  be  connected  singly,  in  series,  or  in  parallel 
as  desired.     The  data  for  the  wires  are  as  follows: 

TABLE  VI 


Coil 

Length 

Number 

Diameter 
in  mils 

Area  in  cir- 
cular mils 

Material 

1 
2 
3 
4 

600  cm. 
300  cm. 
300  cm. 
300  cm. 

36 
30 
30 
36 

5.00 
10.03 
10.03 
5.00 

25.00 
100.5 
100.5 
25.00 

Copper. 
German  silver. 
Copper. 
Copper. 

To  connect  coil  1  in  series  with  a  source  of  electromotive  force, 
connect  the  dry  cell  to  binding  posts  1  and  2,  Fig.  85,  insert 
plugs  1,  2,  and  9,  and  withdraw  plug  10.  When  this  is  done  the 
current  will  flow  through  coil  1  only.  Inserting  plug  10  and 
withdrawing  plug  11  connects  coils  1  and  2  in  parallel.  That 
is,  the  current  can  cross  from  binding  post  1  to  binding  post 
2  by  two  paths.  Inserting  plug  11  and  withdrawing  plug  12 


FIG.  86. 

connects  coils  1,  2,  and  3  in  parallel.     Inserting  plug  12,  when 
other  plugs  are  in,  connects  all  of  the  coils  in  parallel. 

If  it  is  desired  to  connect  coils  1  and  2  in  series,  connect  the 
cell  to  posts  1  and  3,  and  withdraw  plugs  3  and  11.  The  cur- 
rent will  then  flow  from  binding  post  1  to  coil  1,  from  coil  1 
across  plug  10  to  coil  2  and  then  through  coil  2  and  bars  back 
to  binding  post  3.  To  connect  all  coils  in  series  leave  the  cell 
connected  to  binding  posts  1  and  3,  and  remove  plugs  3,  7,  and  11. 
To  connect  coils  1  and  4  in  series  leave  the  battery  connections 


126  MAGNETISM  AND  ELECTRICITY 

as  just  explained  and  remove  plugs  4,  5,  and  6.  Plugs  10,  11, 
and  12  must  be  inserted.  If  it  is  desired  to  connect  coils  1  and 
2,  and  3  and  4  in  parallel  and  then  the  two  parallel  circuits  in 
series,  connect  the  battery  to  binding  posts  1  and  3,  and  with- 
draw plug  5. 

In  using  the  resistance  board  follow  instructions  carefully 
as  this  also  may  be  damaged  by  careless  usage  or  large  currents. 
Study  the  connections  carefully  before  beginning  the  experiment. 

Connect  two  dry  cells,  the  board,  and  volt-ammeter  as  shown 
in  Fig.  86.  That  is,  connect  the  carbon  of  one  dry  cell  to  the 
+  binding  post  of  the  volt-ammeter;  connect  the  zinc  cup  of  this 
dry  cell  to  the  carbon  of  second  cell,  and  the  zinc  cup  of  the 
second  cell  to  one  side  of  a  switch.  The  other  side  of  the  switch 
must  be  connected  to  binding  post  2  of  the  resistance  board  as 
shown  in  Fig.  86.  Finally,  connect  binding  post  1  of  the  board 
to  binding  post  A  of  volt-ammeter.  When  you  have  these 
connections  made,  withdraw  plug  10,  Fig.  85,  push  down  pearl 
push-button  on  volt-ammeter,  and  close  switch  S.  Keep  switch 
closed  until  pointer  quits  swinging,  then  read  the  deflection  and 
immediately  open  the  switch.  Repeat  this  five  times  and  record 
your  readings  thus: 

Experiment  27 
Two  dry  cells  in  series;  Current  through  coil  1 


No. 

of  reading 

Current 

1 
2 
3 
4 
5 

Mean 

0.30  ampere 
0.27  ampere 
0.30  ampere 
0.30  ampere 
0.25  ampere 

1  .  42    ampere 
0  .  284  ampere 

Repeat  the  experiment  with  coil  4  only.  Then  disconnect  the 
wire  from  binding  post  2,  Fig.  85,  and  connect  it  to  binding  post 
3.  Withdraw  plugs  3,  4,  and  6.  Such  a  connection  will  leave 
coils  1  and  4  in  series.  Take  five  readings  as  before  and  record. 
If  you  find  that  some  of  the  readings  differ  greatly,  try  again 
until  you  are  certain  that  the  readings  are  correct. 

In  order  to  get  accurate  readings  it  will  be  necessary  to  have 
the  volt-ammeter  level.     The  pointer  is  not  accurately  balanced 


RESISTANCE  127 

and  unless  care  is  taken  to  keep  the  meter  horizontal  the  readings 
will  be  in  error. 

120.  Theory. — The  results  of  the  foregoing  experiment  show 
clearly  the  change  of  current  when  the  length  of  conductor  is 
changed  and  pressure  remains  constant.  The  wires  of  coils  1 
and  4  are  of  copper  and  of  exactly  the  same  diameters,  but  of 
different  lengths,  see  table  page  125.  The  wire  on  spool  1  is 
just  twice  the  length  of  that  on  spool  4.  Does  the  current  vary 


Low  ftes/sta/ice 


Low  Ftes/sf0fx:e 

•• 

Long  W/re 
/#?/?  ftes/'sfo/ice 

FIG.  87. 

S 

with  the  length?  How?  If  the  experiment  has  been  carefully 
performed,  the  current  through  coil  4  should  be  about  twice 
that  through  coil  1. 

When  coils  1  and  4  are  connected  in  series  the  total  length 
of  the  wire  is  three  times  that  of  the  wire  on  spool  4.  What 
should  the  current  be  if  it  varies  inversely  as  the  length?  Is  the 
current  what  you  expected  it  to  be? 

The  experiment  shows  that  the  current  decreases  as  the  length 


128  MAGNETISM  AND  ELECTRICITY 

of  wire  through  which  it  flows  increases.  This  amounts  to  the 
same  thing  as  to  say  that  the  opposition  offered  by  a  wire  to  the 
flow  of  current  increases  with  the  length  of  the  wire.  This 
opposition  is  called  resistance  and  hence  the  resistance  of  a  con- 
ductor is  directly  proportional  to  its  length.  This  is  clearly 
analogous  to  the  resistance  offered  by  a  pipe  to  the  flow  of  water 
through  it,  the  longer  the  pipe  the  smaller  the  current.  This 
analogy  is  brought  out  clearly  by  Fig.  87. 

121.  Experiment  28.    To  Study  the  Relation  between    Size 
of  Wire  and  Current. 

Apparatus. — Same  as  in  preceding  experiment. 

Operation. — This  experiment  is  to  be  performed  exactly  like 
experiment  27,  but  instead  of  using  coils  1  and  4,  use  coils  3  and  4. 


S/na//  S/'ze  Larae  S/ze 

Low  ftes/stonce 


/7/76»  Wire 


FIG.  88. 

First  connect  two  dry  cells,  board,  meter,  and  switch  as  in 
Fig.  86.  Withdraw  plugs  2,  4,  and  12.  When  this  is  done  the 
current  will  flow  through  coil  3  only.  Hold  down  the  push- 
button on  the  ammeter,  and  close  the  switch.  Read  the  instru- 
ment as  soon  as  the  pointer  comes  to  rest,  then  open  the  switch. 
Coil  3  does  not  have  a  high  resistance  or  a  large  current-carrying 
capacity,  and  hence,  the  current  must  not  be  permitted  to  flow 
through  it  for  more  than  an  instant.  The  pearl  push-button 
on  the  meter  does  not  break  the  main  circuit  and  when  this  is 
released  the  current  will  still  continue  to  flow  through  the  coil 
on  spool  3  unless  switch  S  is  opened.  It  is  thus  necessary  always 
to  open  switch  S  as  soon  as  possible. 

Keep  the  dry  cells  connected  as  before.     Remove  plugs  2,  4, 


RESISTANCE  129 

and  6,  replace  12  and  repeat  the  experiment.  Record  the  de- 
flections exactly  as  in  the  previous  experiment.  Do  the  two 
coils  give  different  deflections?  Which  coil  gives  the  greater 
deflection? 

122.  Theory. — Coils  3  and  4  are  of  copper,  each  300  cm.  long. 
Coil  3  is  of  No.  30  wire  which  has  a  diameter  of  0.01003  in.  or 
10.03  mils,  a  mil  being  1/1000  in.     Coil  4  is  of  No.  36  wire,  and 
has  a  diameter  of  0.005  in.  or  5  mils.     The  results  of  the  experi- 
ment show  that  the  current  through  the  larger,  No.  30,  wire  is 
greater  than  the  current  through  the  No.  36  wire.     The  analogy 
between  the  resistance  offered  by  two  different-sized   pipes  to 
the  flow  of  water,  and  two  different-sized  wires  to  the  flow  of  an 
electric  current  is  shown  in  Fig.  88.     The  exact  relation  between 
the  size  of  wire  and  resultant  current  where  the  pressure  is  kept 
constant  is  not  so  evident.     To  determine  this  relation  we  must 
first  show  how  wires  are  measured. 

123.  Wire  Measurement. — In  this  country  the  length  of  wire 
is  usually  given  in  feet,  and  the  size  is  specified  either  by  diameter, 
cross-sectional  area,  or  gage  number.     The  units  used  for  the 
measurement  of  the  diameter  and  cross-sectional  area  are  not 
the  inch  and  square  inch,  but  the  mil  and  circular  mil. 

The  Mil. — The  unit  of  length  in  measuring  the  diameter  is 
the  1/1000  (  =  0.001)  in.  and  is  called  the  mil.  A  1-in.  cable  has 
a  diameter  of  1,000  mils.  The  diameter  of  a  wire  0.25  in.  is 
equal  to  250  mils,  etc. 

Circular  Mils. — A  circle  whose  diameter  is  0.001  in.  (  =  1  mil) 
is  said  to  have  an  area  of  1  circular  mil.  Since  the  areas  of 
two  circles  having  different  diameters  are  to  each  other  as  the 
squares  of  their  diameters,  to  express  the  cross-section  of  any 
wire  in  circular  mils,  when  its  diameter  in  mils  is  given,  all  that 
is  necessary  is  to  square  the  diameter,  that  is,  multiply  the  di- 
ameter by  itself. 

EXAMPLES 

1.  What  is  the  cross-sectional   area  in  circular  mils  of  a  wire  1/4  in.  in  di- 
ameter? 

Solution.— 

1/4  in.  =0.25  in. 
0.25  in.  =250/1000  =  250  mils 

Area  in  circular  mils  (C.  M.)  equals  diameter  squared 
Dia.  =250  mils 
2502  =  250X250  =  62,500  C.  M. 


130  MAGNETISM  AND  ELECTRICITY 

2.  A  number  0000  wire  has  a  cross-sectional  area  of  211,600  circular  mils. 
What  is  its  diameter  in  mils  and  in  inches? 

Solution.  —  Since  the  cross-sectional  area  in  circular  mils  is  equal  to 
the  square  of  the  diameter  in  mils,  the  diameter  in  mils  must  be 
equal  to  the  square  root  of  the  cross-sectional  area.  In  symbols 

D2  =  area 
and  D  =  V  area 
But  area  =  21  1,600  C.  M. 
Hence  Z>  =  \/21  1,600 

=  460  mils 
1  mil  =  1/1000  in. 

Then  460  mils  =5  =  0.46  in. 


124.  Gage  Numbers.  —  In  the  United  States  practically  the 
only  gage  now  used  for  copper  wire  is  the  American  Wire  Gage 
commonly  called  the  Brown  and  Sharpe  (B.  &  S.)  gage.     This 
gage  was  devised  in  1857  by  Mr.  J.  R.  Brown,  one  of  the  founders 
of  the  Brown  &  Sharpe  Manufacturing  Co.     In  this  gage  the 
size  of  wire  is  specified  by  number.     The  mathematical  law  on 
which  this  gage  is  based  is,  the  ratio  of  any  diameter  to  the 
next  smaller  is  a  constant  number. 

For  practical  purposes  tables  are  prepared  giving  the  gage 
number,  diameter  in  mils  or  inches,  cross-sectional  area  in  circular 
mils,  and  other  data  that  may  be  useful,  depending  upon  the 
completeness  of  the  table.  The  numbers  usually  range  from 
0000  to  40.  The  diameter  of  No.  0000  is  460  mils  and  of  No. 
40,  3.145  mils.  The  student  will  thus  see  that  the  larger  the 
gage  number  the  smaller  the  diameter.  A  wire  table  for  ordinary 
practical  calculations  is  given  on  page  131.  This  table  was  pre- 
pared by  the  Bureau  of  Standards  and  is  published  in  circular 
No.  31  together  with  others  of  greater  accuracy  and  detail. 

125.  Theory.  —  With    this    brief    description    of    methods    of 
measuring  copper  wire  we  shall  be  enabled  to  get  a  relation  be- 
tween current  flowing  and  the  size  of  the  wire  by  means  of  the 
data  of  experiment  28.     Coil  No.  3  has  a  diameter  of  10.03  mils 
and  a  cross-sectional  area  of  100.5  C.  M.     Wire  of  coil  No.  4  has 
a  diameter  of  5  mils  and  a  cross-sectional  area  of  25  C.  M. 
That  is,  wire  of  coil  3  is  just  about  four  times  as  large  as  that  of 
coil  4.     Which  coil  carries  the  larger  current,  and  what  is  the 
ratio  of  the  two  currents?     Does  the  current  strength  have  any 
relation  to  the  size  of  the  wire  when  the  lengths  are  kept  constant? 


RESISTANCE 


131 


Since  we  have  defined  resistance  as  that  property  of  a  con- 
ductor which  opposes  the  flow  of  current,  we  see  that  as  the  larger 
wire  carries  more  current  than  the  smaller,  it  must  offer  less 
resistance  to  the  flow  of  current.  The  experiment  also  shows  that 
the  current  increases  directly  with  the  size.  That  is,  coil  No.  3 
is  made  of  wire  four  times  as  large  as  that  of  coil  4,  and  under 
the  same  conditions  carries  four  times  as  large  a  current.  Since 
the  current  increases  with  the  size  of  the  wire,  the  resistance 
must  decrease  as  the  cross-sectional  area  increases.  Further- 
more, the  area  increases  as  the  square  of  the  diameter,  and  hence 
the  resistance  must  decrease  as  the  square  of  the  diameter  in- 
creases, or,  as  it  is  usually  expressed,  the  resistance  varies  in- 
versely as  the  cross-sectional  area,  or  as  the  square  of  the  diameter. 
The  student  will  see  that  this  is  also  analogous  to  the  resistance 
offered  by  water  pipes  to  the  flow  of  water. 

TABLE  VII.— WORKING  TABLE,  STANDARD  ANNEALED 
COPPER  WIRE 

English  Units 
American  Wire  Gage  (B.  &  S.) 


Gage  No. 

Diameter 
in  mils 

Cross-section, 

Ohms  per  1,000  ft. 

Pounds 
per 
1000  ft. 

Circular 
mils 

Square  in. 

25°  C. 

(  =  77°F.) 

65°  C. 
(  =  149°F.) 

0000 

460.0 

212000.0 

0.166 

0.0500 

0.0577 

641.0 

000 

410.0 

168000.0 

0.132 

0.0630 

0.0728 

508.0 

00 

365.0 

133000.0 

0.105 

0.0795 

0.0918 

403.0 

0 

325.0 

106000.0 

0.0829 

0.100 

0.116 

319.0 

1 

289.0 

83700.0 

0.0657 

0.126 

0.146 

253.0 

2 

258.0 

66400.0 

0.0521 

0.159 

0.184 

201.0 

3 

229.0 

52600.0 

0.0413 

0.201 

0.232 

159.0 

4 

204.0 

41700.0 

0.0328 

0.253 

0.293 

126.0 

5 

182.0 

33100.0 

0.0260 

0.320 

0.369 

100.0 

6 

162.0 

26300.0 

0.0206 

0.403 

0.465 

79.5 

7 

144.0 

20800.0 

0.0164 

0.508 

0.587 

63.0 

8 

128.0 

16500.0 

0.0130 

0.641 

0.740 

50.0 

9 

114.0 

13100.0 

0.0103 

0.808 

0.933 

39.6 

10 

102.0 

10400.0 

0.00815 

1.02 

1.18 

31.4 

11 

91.0 

8230.0 

0.00647 

1.28 

1.48 

24.9 

12 

81.0 

6530.0 

0.00513 

1.62 

1.87 

19.8 

13 

72.0 

5180.0 

0.00407 

2.04 

2.36 

15.7 

14 

64.0 

4110.0 

0.00323 

2.58 

2.97 

12.4 

132 


MAGNETISM  AND  ELECTRICITY 


TABLE  VII— WORKING   TABLE,  STANDARD   ANNEALED 
COPPER  WIRE.— Continued 

English  Units 
American  Wire  Gage  (B.  &  S.) 


Gage  No. 

Diameter 
in  mils 

Cross-section 

Ohms  per  1,000  ft. 

Pounds 
per 
1000  ft. 

Circular 
mils 

Square  in. 

25°  C. 

(  =  77°F.) 

65°  C. 

(=149°R) 

15 

57.0 

3260.0 

0.00256 

3.25 

3.75 

9.86 

16 

51.0 

2580.0 

0.00203 

4.09 

4.73 

7.82 

17 

45.0 

2050.0 

0.00161 

5.16 

5.96 

6.20 

18 

40.0 

1620.0 

0.00128 

6.51 

7.52 

4.92 

19 

36.0 

1290.0 

0.00101 

8.21 

9.48 

3.90 

20 

32.0 

1020.0 

0.000802 

10.4 

12.0 

3.09 

21 

28.5 

810.0 

0.000636 

13.1 

15.1 

2.45 

22 

25.3 

642.0 

0.000505 

16.5 

19.0 

1.94 

23 

22.6 

509.0 

0.000400 

20.8 

24.0 

1.54 

24 

20.1 

404.0 

0.000317 

26.2 

30.2 

1.22 

25 

17.9 

320.0 

0.000252 

33.0 

38.1 

0.970 

26 

15.9 

254.0 

0.000200 

41.6 

48.1 

0.769 

27 

14.2 

202.0 

0.000158 

52.5 

60.6 

0.610 

28 

12.6 

160.0 

0.000126 

66.2 

76.4 

0.484 

29 

11.3 

127.0 

0.0000995 

83.5 

96.4 

0.384 

30 

10.0 

101.0 

0.0000789 

105.0 

122.0 

0.304 

31 

8.9 

79.7 

0.0000626 

133.0 

153.0 

0.241 

32 

8.0 

63.2 

0.0000496 

167.0 

193.0 

0.191 

33 

7.1 

50.1 

0.0000394 

211.0 

244.0 

0.152 

34 

6.3 

39.8 

0.0000312 

266.0 

307.0 

0.120 

35 

5.6 

31.5 

0.0000248 

336.0 

387.0 

0.0954 

36 

5.0 

25.0 

0.0000196 

423.0 

489.0 

0.0757 

37 

4.5 

19.8 

0.0000156 

533.0 

616.0 

0.0600 

38 

4.0 

15.7 

0.0000123 

673.0 

777.0 

0.0476 

39 

3.5 

12.5 

0.0000098 

848.0 

980.0 

0.0377 

40 

3.1 

9.9 

0.0000078 

1070.0 

1240.0 

0.0299 

Note  1. — The  values  given  in  the  table  are  only  for  annealed  copper  of  the 
standard  resistivity.  The  user  of  the  table  must  apply  the  proper  correction 
for  copper  of  any  other  resistivity.  Hard-drawn  copper  may  be  taken  as 
about  2.7  per  cent,  higher  resistivity  than  annealed  copper. 

Note  2. — Ohms  per  mile,  or  pounds  per  mile,  may  be  obtained  by  multi- 
plying the  respective  values  above  by  5.28. 


RESISTANCE  133 

EXAMPLES 

1.  What  is  the  relative  resistance  of  two  wires  each  100  ft.  long,  one  having 
a  diameter  of  20.1  mils  and  the  other  a  diameter  of  5  mils? 

Solution. — Since  the  two  wires  are  of  equal  lengths  their  resistances  will 
vary  only  with  the  squa,re  of  their  diameters.  It  has  just  been  shown 
that  the  larger  wire  has  the  smaller  resistance.  Then  the  wire  whose 
diameter  is  20.1  mils  will  have  the  smaller  resistance,  and  the  ratio  of  the 
two  resistances  will  be  20.  !2-^52  =  404.01 -^25  =  16.1.  Thus  the  smaller 
wire  has  a  resistance  16.1  times  as  great  as  the  larger  wire. 

2.  How  many  times  as  long  must  the  larger  wire  of  problem  1  be  in  order 
that  the  resistances  may  be  equal? 

Solution. — Since  equal  lengths  of  the  two  wires  have  resistances  whose 
ratio  is  1  to  16.1,  and  as  the  resistance  of  a  wire  increases  directly  with  the 
length,  the  larger  wire  must  be  16.1  times  as  long. 

126.  The  Effect  of  Material  upon  the  Resistance  of  Wire.— 

In  discussing  the  water-pipe  analogy  it  was  stated  that  the 
resistance  offered  by  a  pipe  also  depended  upon  the  material  of 
which  it  is  made.  To  determine  whether  wires  of  same  lengths 
and  diameters,  but  of  different  materials,  have  different  elec- 
trical resistances  the  student  must  try  the  following  experi- 
ment. 

127.  Experiment  29.    To  Study  Dependence  of  the  Resist- 
ance of  a  Conductor  on  the  Material  of  Which  it  is  Made. 

Apparatus. — Same  as  in  experiment  28. 

Operation. — Connect  two  dry  cells,  switch,  volt-ammeter, 
and  resistance  board  in  series.  Remove  the  proper  plugs  from 
the  resistance  board  so  that  the  current  must  pass  through  coil 
2.  Close  the  switch  and  read  the  current.  Take  five  readings 
as  in  the  preceding  experiments,  and  obtain  the  mean  value  of 
the  current.  Is  the  current  as  large  as  when  two  cells  were 
connected  in  series  with  coil  3?  In  order  that  the  data  may  be 
obtained  under  like  conditions,  that  is,  pressures  being  the  same, 
determine  what  current  the  two  cells  in  series  will  send  through 
coil  3.  If  data  obtained  at  different  times  are  compared,  they 
may  be  found  to  vary  considerably.  This  may  be  due  to  the 
fact  that  both  the  pressure  and  internal  resistance  of  the  cells 
may  have  changed  in  the  meantime.  Remember  that  the 
current  must  be  permitted  to  flow  through  coil  3  for  only  an 
instant.  Divide  the  numerical  value  of  the  current  through 
coil  3  by  the  value  of  the  current  through  coil  2.  What  is  the 
ratio?  Which  offers  the  higher  resistance,  coil  3  or  coil  2? 


134  MAGNETISM  AND  ELECTRICITY 

128.  Theory. — The  wire  of  coil  2  has  exactly  the  same  length 
and  diameter  as  that  of  coil  3;  the  only  difference  in  the  coils  is 
the  material  of  which  they  are  made.     The  wire  on  spool  3  is  of 
copper  and  on  spool  2  of  German  silver.     German  silver  is  an 
alloy  of  copper,  zinc,  and  nickel.     The  exact   ratio    in   which 
these  metals  are  combined  cannot  be  given,  but  undoubtedly 
there  is  more  copper  than  of  either  of  the  other  two  metals. 

The  results  of  this  experiment  show  that  the  material  of 
which  a  conductor  is  made  determines  the  current  that  a  given 
pressure  will  send  through  a  wire  of  given  cross-section  and 
length.  The  resistance  thus  also  depends  upon  the  material. 
This  also  is  clearly  analogous  to  the  cases  of  water  pipes. 

129.  Unit  of  Resistance. — In  order  to  be  able  to  measure,  or 
compare  resistances,  some  unit  of  resistance  must  be  chosen. 
The  practical  unit  is  called  the  ohm.     The  ohm  is  the  resistance 
offered  to  the  flow  of  an  unvarying  electric  current  by  a  column 
of  mercury  106.3  cm.  long,  14.4521  grm.  mass,  and  of  constant 
cross-sectional  area,  at  the  temperature  of  melting  ice.     This 
is  a  definite  unit  and  other  resistances  are  expressed  in  terms 
of  it. 

130.  Calculation    of   Resistance. — We    have    seen    that    the 
cross-sectional    area   of   electrical    conductors   is   measured   in 
circular  mils  and  the  length  in  feet.     We  can  thus  consider  a 
piece  -of  wire  1  ft.  long,  1  mil  (0.001  in.)  in  diameter  as  a  unit  of 
conductor.     The  resistance  in  ohms  per  foot  of  annealed  copper 
wire  1  mil  in  diameter  is  9.61  ohms   at  0  degrees  cent.  =  32 
degrees  Fahrenheit,  or  10.371  ohms  at  20  degrees  cent.     This 
resistance  is  sometimes  called  "  specific  resistance."     A  better 
name  is  resistivity. 

As  we  have  seen,  the  resistance  of  wire  of  uniform  cross- 
section  increases  directly  with  the  length  (results  of  experiment 
27).  Ten  feet  of  annealed  copper  wire  1  mil  in  diameter  will 
have  a  resistance  of  ten  times  9.61  or  96.1  ohms.  If  I  is  the 
length  in  feet,  the  resistance  of  I  feet  of  the  same  wire  will  be 
9.61X1. 

Again  the  results  of  experiment  28  show  that  the  resistance 
decreases  directly  as  the  cross-sectional  area  of  the  wire  in- 
creases. Thus  if  we  take  a  wire  whose  diameter  is  2  mils,  its 
cross-sectional  area  will  be  22  =  2X2  =  4  C.  M.  and  its  resistance 
will  be  1/4  of  9.61  =  2.4  ohms.  In  general,  if  1  ft.  of  copper 
wire  has  a  cross-sectional  area  of  A  circular  mils,  its  resistance 


RESISTANCE  135 

9.61 
will  be^-7—  ohms.     We  have  just  seen,  however,  that  a  wire  I 

feet  long  will  have  a  resistance  I  times  as  large.  We  can  thus 
say  that  the  resistance  of  copper  wire  at  a  temperature  of  0 
degrees  cent,  is  given  by 

9.6U 

— A —  onms 

where  I  is  in  feet  and  A  in  circular  mils. 

EXAMPLES 

1 .  What  will  be  the  resistance  of  2,500  ft.  of  No.  12  copper  wire? 
Solution. — No.  12  wire  has  a  cross-sectional  area  of  6,530  C.  M.     The 
resistance  in  ohms  at  0  degrees  cent,  is 

9.61X2500 

6530 
#=3.7  ohms 

2.  In  wiring  a  house  3,500  ft.  of  wire  0.064  in.  in  diameter  is  used.     What 
is  the  resistance  of  this  wire  at  20  degrees  cent.  ? 

Solution. — According  to  the  formula 

10.371XZ 

R=  -^AT 

I  =3,500  ft. 

A=642  =  64X64=4,096C.  M. 
„     10.371  X  3500 
Hence  R  = Tnog =  8.8  ohms 

3.  How  long  must  a  German  silver  wire  be  to  have  a  resistance  of  40  ohms 
if  it  is  81  mils  in  diameter  and  if  the  resistivity  of  German  silver  is  125.7 
ohms? 

Solution. — The  formula  for  the  resistance  of  German  silver  wire  is 

125.7 1 


Solving  this  for  I  we  get 

AXR 
"125.7 
R  =40  ohms 
A  =81X81=6,561  C.  M. 

40X6561 
Hence  I        ~i25?T~ 

/  =209  ft.,  nearly 

131.  Resistivity  or  Specific  Resistance. — In  the  foregoing  dis- 
cussion the  resistance  of  1  ft.  of  annealed  copper  wire  1  mil  in 
diameter  was  stated  to  be  9.61  ohms  at  0  degrees  cent.  This 
quantity  is  called  resistivity  or  specific  resistance  as  it  depends 


136 


MAGNETISM  AND  ELECTRICITY 


upon  the  material  of  which  the  conductor  is  made.  Thus  when 
we  desired  to  find  the  resistance  of  German  silver,  125.7  was  used 
for  the  resistivity.  This  is  because  a  German  silver  wire  of  the 
same  length  and  size  as  a  copper  wire  will  have  a  resistance  about 
13.2  times  as  high. 

The  resistivity  of  metals  will  depend  upon  their  purity  and 
temperature.  The  resistivity  of  alloys  such  as  German  silver 
will  depend  upon  the  composition  of  the  alloys.  The  resistivity 
of  some  of  the  most  common  metals  is  given  in  Table  VIII. 

TABLE  VIII.— RESISTIVITY  OF  METALLIC  WIRES 


Substance 

Resistance  in  ohms  at  0  degrees 
cent,  of  a  wire  1  ft.  long 
1  mil  in  diameter 

Aluminum,  annealed  

15.8 
213.1 

787.5 
9.61 
9.86 
12.56 
12.78 
65.21 

125.7 
58.31 
115.1 
565.9 
74.78 
54.35 
8.781 
9.538    «n.     v»« 

Antimony,  pressed.  . 

Bismuth  pressed 

Copper,  annealed  

Copper,  hard  drawn 

Gold,  annealed  

Gold,  hard  drawn 

Gold-silver,  2  parts  gold  1  part  silver, 
by  weight. 
German  silver 

Iron  

Lead 

IVIercury 

Nickel  .                                        

Platinum 

Silver,  annealed  

•hrer.  hard  drawn  .  . 

1' 

:! 


! 


132.  Change  of  Resistance  with  Temperature. — The  student 
will  notice  that  the  definition  of  the  ohm  specifies  that  the  tem- 
perature must  be  that  of  melting  ice,  that  is,  0  degrees  cent. 
Likewise  the  resistivities  given  in  the  above  table  are  correct 
only  when  the  temperature  is  0  degrees  cent.     The  question 
naturally  arises,  how  does  the  resistance  change  with  temperature? 

133.  Experiment  30.    To  Study  Effect  of  Temperature  upon 
Resistance. 

Apparatus. — Same  as  in  experiment  29. 

Operation. — Connect  three  dry  cells  in  series  with  the  volt- 
ammeter  and  resistance  board  exactly  as  in  experiment  29  except 
that  the  current  is  to  pass  through  coil  1  in  place  of  coil  2.  Take 
a  watch  or  some  other  convenient  timepiecee  and  place  it  where 


RESISTANCE  137 

you  can  observe  the  time.  Having  adjusted  the  apparatus  care- 
fully, press  down  the  push-button  on  the  volt-ammeter  and  close 
the  switch.  Observe  carefully  the  value  of  the  current  just  as 
soon  as  the  pointer  comes  to  rest.  Leave  the  switch  closed  for 
about  20  seconds,  one-third  of  a  minute.  Under  no  circumstances 
must  the  switch  be  closed  longer  than  half  a  minute.  Just 
before  opening  the  switch  read  the  ammeter  and  note  if  the 
current  has  increased  or  decreased.  Feel  of  the  coil  and  notice 
if  it  is  warm.  If  the  switch  should  be  left  closed  too  long  the 
coil  may  become  hot  enough  to  burn  off  the  insulation,  hence, 
the  necessity  of  observing  the  time. 

After  the  coil  has  become  cool,  repeat  until  you  are  certain 
that  the  current  decreases.  The  decrease  in  the  current  will 
not  be  great  but  should  be  noticeable. 

134.  Theory. — Coil  No.  1  is  of  copper  wire  600  cm.  long  and 
offers  considerable  resistance  to  the  flow  of  the  current.  The 
current  that  passes  through  it  when  three  cells  are  connected 
in  series  is  not  over  one-half  an  ampere  at  the  start.  This 
current,  however,  slowly  decreases  if  the  circuit  is  left  closed  for 
a  brief  time.  There  can  be  only  two  causes  for  this,  either  the 
pressure  of  the  dry  cells  has  changed,  or  the  resistance  of  the 
coil  has  changed.  That  the  change  in  current  is  not  due  to  a 
change  in  the  pressure  of  the  cells  can  be  shown  easily  by  measur- 
ing the  pressure  before  and  after  the  experiment.  (See  page  93.) 

If  the  pressure  is  measured  it  will  be  seen  that  the  voltage  shows 
no  appreciable  change.  The  change  in  current  must  then  be 
due  to  a  change  in  resistance.  The  current  decreases,  and  there- 
fore the  resistance  must  increase.  The  student  observed  that 
the  coil  became  quite  warm,  and  hence  its  temperature  must  haVeJ 
been  quite  high.  In  short,  then,  we  can  say  that  the  resistance 
of  copper  increases  as  the  temperature  increases.  If  measure- 
ments were  made  on  other  metals  the  same  relation  would  be 
found  to  hold. 

The  resistance  of  pure  metals  increases  with  the  rise  in  tempera- 
ture. For  purposes  of  calculation  the  change  in  the  resistance 
of  1  ohm  for  a  change  of  1  degree  cent,  in  temperature  has 
been  carefully  measured  by  the  Bureau  of  Standards  and  for 
this  change  is  approximately  the  same  for  each  metal.  Its  nu- 
merical value  for  annealed  copper  is  about  0.00393.  Thus  the 
change  in  the  resistance  of  the  wire  on  coil  1  is  approximately 
0.393  of  1  per  cent  for  every  centigrade  degree  change  in  tempera- 


m 


138  MAGNETISM  AND  ELECTRICITY 

ture.     If  the  coil  has  a  resistance  of  10  ohms  at  0  degrees  cent, 
its  resistance  at  100  degrees  cent,  will  be 

10+10X0.00393X100  =  13.93  ohms. 

These  principles  can  be  formulated  thus:  If  R0  is  the  resist- 
ance of  a  wire  at  0  degrees  cent,  its  resistance  Rt  at  t  degrees 
cent,  will  be  equal  to  R0  plus  the  increase.  This  increase,  as 
has  been  shown,  is  .00393  ohm  for  every  ohm  for  1  degree; 
hence  the  increase  in  R0  ohms  for  1  degree  change  in  tempera- 
ture will  be  0.00393  R0,  and  for  t  degrees  it  will  be  0.00393  R0  t. 
The  total,  or  Rt,  resistance  is  then 

#,  =  #0+0.00393  Rot 
=  R0  (1+0.003930 

EXAMPLE 

A  copper  coil  has  a  resistance  of  200  ohms  at  0  degrees  cent.  What  is  its 
resistance  at  100  degrees  cent.  ? 

Solution.— 

Ro  =200  ohms 
t    =100 
Rt      is  required 
Rt   =200(1+0.00393X100) 

=  200(1+0.393)  =278.6  ohms 

135.  Practical  Applications. — This  example  shows  that  the 
change  in  resistance  due  to  a  change  in  temperature  must  be 
taken  into  consideration  in  the  design  of  •electrical  apparatus, 
and  also  in  many  electric  problems. 

Any  one  who  has  had  experience  with  generators  knows  that 
if  the  field  current  is  adjusted  while  the  field  winding  is  cold,  in 
a  short  time  further  adjustment  may  be  necessary.  The  reason 
for  this  is  very  evident.  The  current  through  the  field  is  deter- 
mined by  the  rheostat  resistance  and  field  resistance.  When 
the  current  is  first  adjusted  to  give  full  voltage  the  resistances  of 
rheostat  and  field  winding  are  lower  than  after  the  current  has 
been  flowing  through  them  for  a  short  time.  The  current  heats 
the  wire,  increasing  its  resistance  as  explained,  and,  as  the  resist- 
ance increases,  the  current  must  decrease,  thus  necessitating 
further  adjustment. 

In  using  a  voltmeter  to  measure  the  voltage  of  a  circuit  it 
is  advisable  to  keep  its  circuit  closed  only  while  the  reading  is 
being  taken.  If  the  circuit  is  kept  closed  for  some  time  the 


RESISTANCE  139 

windings  of  the  voltmeter  will  increase  in  temperature  and  con- 
sequently a  smaller  current  will  flow  through  the  instrument. 
Since  the  deflection  of  the  instrument  depends  upon  the  current 
flowing  through  it,  the  deflection  will  be  in  error. 

Somewhat  the  same  thing  is  true  of  watthour  meters.  If  a 
watthour  meter  is  tested  immediately  upon  being  connected  to 
the  circuit  and  again  after  having  been  in  service  for  an  hour, 
it  will  be  found  that  it  no  longer  registers  the  same.  One  reason 
for  this  is  that  the  voltage  coil  has  changed  its  resistance  by  being 
heated  by  the  pressure  current.  It  is  thus  necessary  to  leave 
the  meter  in  circuit  for  some  time  before  testing  in  order  that  the 
pressure  coil  may  reach  a  constant  temperature. 

Another  most  important  practical  application  of  this  principle 
is  the  measurement  of  high  temperatures.  For  this  purpose, 
platinum  wire  is  used.  The  wire  is  wound  upon  a  mica  frame 
and  incased  in  a  porcelain  tube  as  shown  in  Fig.  89.  To  measure 


Porcelain  Tube. 


Platinum  'winding 
FlG.  89. 

the  temperature  in  an  annealing  oven,  for  instance,  the  resist- 
ance of  the  platinum  wire  is  determined  at  zero  cent,  tempera- 
ture, and  then  again  at  the  temperature  of  the  oven.  The 
temperature  is  then  obtained  by  dividing  the  difference  in  the 
resistance  by  the  resistance  at  zero  degrees  times  the  resistance 
temperature  coefficient  of  platinum.  By  such  means  tempera- 
tures as  high  as  1200  degrees  cent,  can  be  quite  accurately 
measured.  The  principle  can  be  illustrated  by  an  example. 

EXAMPLE 

The  resistance  of  the  armature  of  a  certain  motor  at  0  degrees  cent,  is  1.7 
ohms.  After  a  run  of  a  few  hours  the  resistance  is  again  measured  and  is 
found  to  be  1.98  ohms.  What  is  the  temperature  of  the  winding? 

Solution.  —  The  change  in  resistance  is  1.98  —  1.7=0.28  ohms.  The 
change  in  resistance  for  1  ohm  for  1  degree  cent,  is  0.00393  ohm;  for  1.7  ohms 
it  is  .00393X1.7=0.006681  ohm.  Since  the  total  change  is  0.28  ohms  the 
change  in  temperature  will  be  approximately 

0  28 
14 


00668  1  cent> 


140 


MAGNETISM  AND  ELECTRICITY 


136.  Temperature  Coefficient  of  Resistance. — The  change 
in  the  resistance  of  1  ohm  for  a  change  of  1  degree  in  temperature, 
discussed  in  the  foregoing,  is  called  the  resistance  temperature 
coefficient.  For  commercial  copper  wire  the  American  Institute 
of  Electrical  Engineers  has  adopted  the  value  0.00393.  As 
already  pointed  out,  this  is  approximately  the  resistance  tempera- 
ture coefficient  for  most  pure  metals,  except  the  magnetic  metals. 
For  iron  the  temperature  coefficient  is  0.00625  per  degree  cent. 

An  alloy  has  a  much  lower  temperature  coefficient,  and  to  a 
large  extent  its  value  depends  upon  the  metals  that  are 
combined  and  also  upon  their  ratio  of  combination.  The  tem- 
perature coefficient  of  German  silver  may  be  considered  to  be 
approximately  one-tenth  as  large  as  that  of  copper.  An  alloy 


Voltage 

FIG.  90. 

consisting  of  84  per  cent  copper,  12  per  cent  manganese,  and  4 
per  cent  nickel,  has,  at  ordinary  temperatures,  a  very  small 
temperature  coefficient,  which  at  higher  temperatures  becomes 
zero,  and  finally  negative;  that  is,  the  resistance  finally  decreases 
with  increases  of  temperature.  This  alloy  called  manganin  is 
used  almost  exclusively  in  standard  resistances  and  also  in 
electrical  measuring  instruments. 

Many  substances  have  a  negative  temperature  coefficient. 
That  is,  their  resistance  decreases  as  the  temperature  increases. 
Carbon,  of  which  the  filament  of  the  carbon  incandescent  lamp 
is  made,  is  one  of  these  substances.  The  resistance  temperature 
coefficient  of  the  material  of  the  metallic  filament,  such  as  tungsten 
lamps,  is  positive.  The  change  in  resistance  with  voltage  of 
these  two  kinds  of  filaments  is  shown  in  Fig.  90. 


RESISTANCE  141 

The  resistance  of  all  electrolytes  decreases  with  rise  of  tem- 
perature, and  the  same  thing  is  true  of  substances  commonly 
called  insulators. 

137.  Resistance  of  Contacts. — When  two  conductors  are  joined 
and  an  electric  current  is  passed  through  the  junction,  a  drop 
of  voltage  will  result.  The  laws  of  this  contact  drop  have 
recently  been  investigated  by  Mr.  F.  W.  Harris,  who  states  the 
results  of  his  investigations  in  the  form  of  four  laws:1 

1.  All  other  conditions  being  constant,  the  voltage  across  a 
contact  joint  will  increase  directly  with  the  current. 

2.  Where  the  conditions  of  the  surface  in  contact  are  not 
affected  thereby,  the  voltage  across  a  contact  will  vary  inversely 
with  the  pressure. 

3.  The  resistance  between  materials  depends  directly  upon 
the  resistivity  of  the  materials,  those  having  a  low  resistivity 
having  also  a  low  contact  resistance. 

4.  The  resistance  between  contacts  depends  not  upon  their 
area,  but  only  on  the  total  pressure  with  which  they  are  forced 
together. 

The  results  stated  in  law  1  merely  show  that  the  effect  of  a 
contact  upon  current  flow  is  the  same  as  that  of  a  resistance 
and  hence  may  properly  be  treated  as  such. 

Law  2  shows  that  the  more  closely  the  surfaces  are  pressed 
together,  the  less  the  pressure  drop  across  the  junction.  This 
shows  the  necessity  of  keeping  all  electrical  contacts  clean  and 
tight.  Many  a  piece  of  electrical  apparatus  has  failed  to  give 
satisfactory  service  on  account  of  a  loose  contact. 

At  first  reading  it  may  seem  that  law  4,  which  is  new,  does 
not  express  the  facts,  for  it  is  common  practice,  in  the  design 
of  switches,  to  limit  the  current  density  to  50  or  75  amperes  per 
square  inch  at  the  switch  contacts.  This  is  done  for  the  purpose 
of  reducing  the  voltage  drop  at  the  contacts  to  a  minimum. 
According  to  law  4  the  voltage  drop  across  the  contacts  can  be 
reduced  greatly  by  increasing  the  pressure  between  the  jaws  and 
the  blade  of  the  switch.  Practical  requirements  of  construction 
and  operation  limit  the  pressure  to  which  the  junctions  can  be 
subjected. 

RECAPITULATION 

1.  Electrical  resistance  is  the  property  of  a  conductor  by  virtue  of  which 
it  opposes  the  passage  of  electricity  through  it.  At  constant  temp- 
1  Electrical  Journal,  July,  1913,  page  637. 


142  MAGNETISM  AND  ELECTRICITY 

erature  the  resistance  of  a  conductor  is  directly  proportional  to  its 
length  and  inversely  proportional  to  its  cross-sectional  area. 

2.  Resistivity  or  specific  resistance  is  the  characteristic  propriety  of  a 
substance  upon  which  the  resistance  of  a  conductor  formed  of  this 
material  depends.     For  purposes  of  measurement  the  unit  of  re- 
sistivity is  taken  as  the  resistance  of  a  conductor  of  unit  length  and 
unit  cross-sectional  area.     In  practical  work  the  unit  length  is  usually 
1  ft.  and  unit  cross-section  is  1  circular  mil.     In   scientific  calcula- 
tions 1  cm.  is  taken  as  the  unit  length  and  square  centimeter  as  the 
unit  cross-section. 

3.  The  mil  is  the  unit  of  length  used  in  measuring  the  diameters  of 
wires.     It  is  equal  to  1/1000  in. 

4.  The  circular  mil  is  the  unit  area  used  in  measuring  the  cross-sectional 
area  of  wires.     The  circular  mil  is  equal  to  the  area  of  a  circl6  1 
mil  in  diameter. 

5.  The  ohm  is  the  unit  of  resistance.    The  ohm  is  defined  as  the  resist- 
ance offered  to  the  flow  of  an  unvarying  electric  current  by  a  column 
of  mercury  106.3  cm.  long,  14.4521  grm.  mass,  of  constant  cross- 
sectional  area  and  at  the  temperature  of  melting  ice.  . 

6.  The  resistance  of  wires  at  a  temperature  of  0  degrees  cent,  may  be 
calculated  by  the  following  formula  : 


where  r  is  the  resistivity  of  the  material  at  0  degrees  cent.,  I  the  length, 
and  A  the  cross-sectional  area. 

7.  The  resistance  of  most  conductors  changes  with  temperature.     The 
change  in  one  ohm  caused  by  a  change  of  1  degree  cent,  is  called  the 
temperature   coefficient   of  resistance.     The   temperature   coefficient 
of  metals  is  positive  and  approximately  the  same  for  all  pure  metals. 
Non-metals  and  electrolytes  have  a  negative  temperature  coefficient. 

8.  When  two  surfaces  are  joined  and  a  current  is  passed  at  right  angles 
to  the  surfaces  a  loss  of  voltage  will  result  at  the  junction.     The 
cause  of  the  voltage  drop  is  called  contact  resistance.    This  voltage 
drop  takes  place  in  accordance  with  the  following  laws  : 

(a)  All  other  conditions  being  constant,  the  voltage  across  a  contact 
joint  increases  directly  with  the  current;  or,  the  joint  between  two 
materials  behaves  exactly  like  a  resistance. 

(b)  Where  the  conditions  of  the  surface  are  not  affected  thereby, 
the  voltage  drop  across  a  contact  will  vary  inversely  with  the  pressure. 

(c)  The  resistance  between  materials  depends  directly  on  the  resis- 
tivity of  the  materials;  those  having  a  low  resistivity  also  have  a 
low  contact  resistance. 

(d)  The  resistance  between  contacts  depends  not  upon  their  area, 
but  only  on  the  total  pressure  with  which  they  are  forced  together. 


CHAPTER  VIII 

FLOW  OF  CURRENT  IN  A  CIRCUIT 

138.  Introduction.  —  So  far  we  have  learned  that  the  flow  of 
current  through  or  along  a  conductor  depends  upon  the  electrical 
pressure  applied,  and  when  the  pressure  is  continuous  or  direct, 
upon  the  resistance  of  the  circuit.     It  has  also  been  shown  that 
the  property  of  a  conductor  called  resistance  is  determined  by 
the  material,  length,  and  cross-sectional  area  of  the  conductor. 
Nothing  has  so  far  been  said  about  the  exact  or  numerical  rela- 
tion between  current,  pressure,  and  resistance.     This  relation 
was  first  investigated  by  Dr.  G.  S.  Ohm,  in  1827,  and  is  known 
as  Ohm's  law. 

139.  Ohm's  Law.  —  In  experiment  29  it  was  shown  that  when 
two  cells  were  connected  in  series  with  coils  2  and  3  of  the  resist- 
ance board,  successively,  the  currents  through  the  coils  differed 
greatly,  the  greater  current  flowing  through  coil  3.     This  was 
explained  by  saying  that  coil  2   offered  higher  resistance  to 
the  passage  of  the  current,  or  that  coil  2  had  many  times  the 
resistance  of  coil  3.     Since  the  only  quantities  that  we  have 
measured  are  electrical  pressure  and  current,  the  resistance  of 
the  circuit  may  be  looked  upon  as  the  ratio  of  the  pressure  to 
the  current.     In  algebraic  symbols  we  can  write  this  as  follows: 


T>    .  , 
Resistance 


R=  Y  or 

Electrical  Pressure 


^  — 
Current 


where  R  stands  for  resistance,  E  for  electrical  pressure,  and  / 
for  the  current.  This  expression,  or  the  relation  between  current, 
pressure,  and  resistance,  is  known  the  world  over  as  Ohm's  law. 
If  the  pressure  is  given  in  volts  and  the  current  in  amperes,  the 
resistance  R  is  given  in  ohms.  This  expression  is  of  the  greatest 
importance  in  all  electrical  calculations,  and  accordingly  we  are 
justified  in  giving  a  comparatively  extended  discussion  of  it. 
Ohm's  law  stated  in  simple  words  means  that  in  any  circuit  the 
pressure  bears  a  constant  relation  to  the  current.  It  may  be 
15  143 


144 


MAGNETISM  AND  ELECTRICITY 


stated  another  way;  for  instance,  the  expression  may  be  written 
in  the  form 


~R 

which  is,  perhaps,  the  most  common.  This  expression  means 
that  the  current  I  is  equal  to  the  pressure  E  divided  by  the  resist- 
ance R.  We  can  then  say  that  when  R  is  constant,  7,  the  current, 
will  increase  or  decrease  as  E}  the  pressure,  increases  or  decreases. 
Doubling  E  will  double  the  current,  etc.  Again  if  the  pressure 
E  remains  constant,  the  current  I  will  vary  inversely  as  the 
resistance  R,  increasing  when  R  decreases  and  decreasing  when 
R  increases.  This  relation  can  be  easily  verified  by  a  simple 
experiment  as  follows: 

140.  Experiment  31.    To  Verify  Ohm's  Law. 
Apparatus.  — 

Three  dry  cells 

Volt-ammeter 

Resistance  board 

Switch 

Connecting  wires 


FIG.  91. 

Operation. — First  connect  one  fresh  dry  cell  as  indicated  in  Fig. 
91.  Leave  switch  S  open  at  first,  and  remove  plugs  12,  11,  and 
8.  Press  down  on  pearl  push-button  P  and  insert  plug  12.  This 
connection  will  give  current  through  coil  3.  Read  and  record 
this  current.  Now  release  the  push-button  and  close  switch  S. 


FLOW  OF  CURRENT  IN  A  CIRCUIT  145 

This  will  give  the  voltage  applied  to  coil  3.  Read  and  record 
this  voltage,  also. 

Next  connect  two  dry  cells  in  series  in  place  of  the  one  cell. 
Again  measure  the  current  through  coil  3  and  the  voltage  as 
before.  It  will  be  well  to  take  three  or  four  readings  of  current 
and  also  three  or  four  readings  of  the  voltage  in  order  that  an 
average  value  may  be  obtained. 

Always  remove  plug  12  as  soon  as  a  reading  is  made.  This 
breaks  the  current  circuit  and  avoids  heating  the  coil.  Compare 
the  currents  and  voltages  in  the  two  sets  of  readings.  When 
two  cells  are  used,  how  does  the  voltage  compare  with  the 
voltage  when  one  cell  is  used?  Has  the  current  increased  as 
the  pressure?  Next  insert  plug  8,  remove  plug  9,  and  repeat 
the  experiment.  This  connection  will  send  the  current  through 
coil  4.  Record  the  values  of  current  and  pressure. 

The  resistance  of  coil  3  is  about  1  ohm  and  that  of  coil  4  is 
about  4  ohms.  In  each  case  divide  the  voltage  by  the  resistance 
and  see  if  the  current  is  approximately  given  by 

7-^ 

R 

141.  Theory. — As  the  preceding  experiment  shows,  the  cur- 
rent strength  is  directly  proportional  to  the  pressure  applied. 
It  is  possible  to  make  a  perfectly  general  statement  of  this  law. 
Thus  in  general  one  may  say  that  the  current  strength  in  any 
circuit  is  directly  proportional  to  the  sum  of  all  the  electromotive 
forces  in  the  circuit.  This  relation  expressed  algebraically  is 

E  =  KI 

E 
or  -j  =  K,  a  constant 

This  holds  for  both  direct  and  alternating-current  circuits  so 
long  as  the  physical  conditions  surrounding  the  circuit  remain 
unchanged.  For  direct-current  circuits  K  is  equal  to  what  is 
called  the  resistance  of  the  circuit  and  under  these  conditions 

E  =  RI 

E 
or  -j  =  R 

Thus  the  ratio  of  the  electromotive  force  to  current  is  constant 
so  long  as  physical  conditions  remain  constant.  If,  for  instance, 
the  temperature  changes,  this  ratio  will  change.  This  is  ex- 
plained by  saying  that  the  resistance  changes. 


146  MAGNETISM  AND  ELECTRICITY 

In  alternating-current  circuits  the  total  e.m.f.  must  include 
the  e.m.f.'s  of  mutual  induction,  self  induction,  and  capacity. 
When  these  are  considered  Ohm's  law,  as  stated,  still  holds. 

In  applying  Ohm's  law  to  the  solution  of  electrical  problems, 
all  or  the  algebraic  sum  of  all  of  the  pressures  that  may  be 
included  as  well  as  all  of  the  resistances,  must  be  considered. 
The  student  will  readily  understand  this  if  he  will  perform 
experiment  31  in  a  little  different  way.  First  measure  the 
electromotive  force  of  one  cell  as  shown  in  Fig.  63.  Divide 
this  pressure  by  1  ohm  and  compare  the  result  with  the  current 
through  coil  3  which  was  obtained  in  the  first  part  of  the  experi- 
ment. The  result  is  considerably  larger  than  the  current 
measured.  This  is  due  to  the  fact  that  the  connecting  wires 
and  cell  have  some  resistance  which  is  not  considered.  An 
examination  of  the  circuit  will  show  that  the  current  flows  from 
the  zinc  plate,  or  cup,  of  one  cell  through  the  electrolyte  to  the 
carbon  rod  in  the  center;  then  through  the  connecting  wire  to 
the  next  cell,  through  its  electrolyte,  through  the  binding  screws 
and  connecting  wires  to  the  ammeter;  then  through  wires  con- 
necting ammeter  and  resistance  board,  through  resistance  coil 
and  back  to  the  cell.  If,  in  such  a  case,  we  know  the  value  of  the 
separate  pressures  and  resistances  that  are  in  series,  we  can 
calculate  the  current  by  dividing  the  sum  of  the  pressures  by  the 
sum  of  the  resistances. 

EXAMPLES 

1.  Let  there  be  5  cells  in  series,  each  having  a  pressure  of  1.4  volts  and  an 
internal  resistance  of  0.5  ohm.     If  the  resistance  of  the  connecting  wires 
is  1.5  ohms,  what  current  will  flow  through  a  coil  of  5  ohms  resistance? 

Solution. — The  total  pressure  is  equal  to  5X1.4  =  7  volts.  The  total 
internal  resistance  of  the  cells  is  0.5X5=2.5  ohms.  The  resistance  of 
the  circuit  is  then 

72  =  1.5+2.5+5  =  9  ohms 
The  current  is  given  by 

ET 

/  =  D  =  7/9  ampere 

2.  The  counter  pressure  of  a  lead  storage  cell  is  2.3  volts;  its  internal  resist- 
ance is  0.05  ohm.     How  much  current  will  4  dry  cells  send  through  the 
storage  cell  if  each  dry  cell  has  an  internal  resistance  of  1  ohm,  polariza- 
tion to  be  neglected  ? 


FLOW  OF  CURRENT  IN  A  CIRCUIT  147 

Solution.  —  The  voltage  of  the  4  cells  in  series  is 
4X1.4  =  5.6  volts 

The  resultant  pressure  is  the  difference  between  this  voltage  and  the 
counter  pressure  of  the  storage  cell;  this  is 

5.6-2.3  =  3.3  volts 
The  total  resistance  is 

4X1+0.05  =  4.05  ohms 
The  current  is  then 

3.3  -^  4.05  =0.8  ampere 

It  is  very  evident  that  by  means  of  Ohm's  law  any  one  of  the 
three  quantities  I,  E,  and  R  can  be  determined,  provided  the 
other  two  are  known.  Thus,  in  experiment  31,  the  pressure 
E  was  measured,  and  R  was  given.  The  value  of  the  resistance 
of  coil  2,  or  any  other  coil  on  the  board  can  be  determined  by 
measuring  the  pressure  applied,  and  then  connecting  the  ap- 

paratus as  in  Fig.  91  and  measuring  the  current.     The  resistance 

W 
of  the  coil  is  then  equal  to  R=  j  ohms,  or  pressure  divided  by 

resistance.     In  this  case  R,  of  course,  includes  the  resistance  of 
the  connecting  wires. 

EXAMPLES 

1.  What  is  the  resistance  of  a  60-  watt  carbon  incandescent  lamp  when  a 
110-volt  pressure  gives  a  current  of  0.55  amperes? 

Solution.  — 


#  =  110  volts 
/  =0.55  ampere 

£=,^1=200 

2.  A  storage  battery  whose  e.m.f.  is  24  volts  and  internal  resistance  0.6  ohm 
is  connected  to  a  wire  whose  resistance  is  5  ohms;  what  is  the  current? 
What  is  the  voltage  between  the  ends  of  the  wire? 

Solution.  — 

#  =  24  volts 

#  =  0.6+5  =  5.6  ohms 

E 


Then 


24 

=^-77  =  4.3  amperes  (nearly) 
o.o 


From  Ohm's  law  we  also  have 
E=RXI 


148  MAGNETISM  AND  ELECTRICITY 

That  is,  the  pressure  drop  along  a  resistance  is  equal  to  the  resistance 
times  the  current.  The  wire  resistance  is  5  ohms  and  current  is  4.3 
amperes;  hence,  the  voltage  between  wire  ends  is  5  X4.3  =21.5  volts. 

3.  A  battery  whose  e.m.f.  is  8  volts  delivers  2  amperes  to  a  circuit  of  3.6 
ohms  resistance.     What  is  the  internal  resistance  of  the  cell? 

Solution. — The  pressure  drop  across  resistance  is  3.6  X2  =  7.2  volts.  The 
battery  drop  must  be  8  —  7.2=0.8  volts,  and  the  battery  resistance  by 
Ohm's  law  must  be  0.8-7-2=0.4  ohm. 

4.  The  open  circuit  voltage  of  a  storage  battery  is  11  volts.     This  battery 
will  send  a  current  of  4  amperes  through  a  coil  at  a  pressure  of  10  volts. 
What  is  the  battery  resistance? 

Solution. — The  voltage  spent  in  forcing  the  current  through  the  battery  is 
11-10  =  1  volt 

then  fl  =  y  =  l/4 

R  =  0.25  ohms 

142.  Capacity. — In  Article  141  it  was  stated  that  in  alternating 
current  circuits  the  total  e.m.f.  must  include  the  e.m.f. 's  of 
mutual  induction,  self-  induction,  and  capacity.  The  effect  of 
mutual  induction  and  self  induction  has  already  been  mentioned, 
but  the  subject  of  capacity  and  its  influence  has  not  been 
explained. 

If  two  metal  plates  be  separated  by  a  good  insulator,  and 
the  two  plates  be  connected  to  a  source  of  electrical  pressure,  a 
momentary  current  will  flow  into  the  plates  which  will  become 
positively  and  negatively  charged.  The  intensity  of  the  momen- 
tary current  will  depend  upon  the  ability  of  the  plates  to  hold  a 
charge  of  electricity.  This  ability  of  a  conductor  or  a  system 
of  conductors,  to  store  electricity  is  called  electrical  capacity. 
A  system  of  conductors  arranged  as  indicated  in  Fig.  92,  is  called 
a  condenser.  The  capacity  of  a  condenser  is  determined  by  the 
arrangement,  number,  and  size  of  the  conducting  plates  as  well 
as  the  thickness  and  material  of  the  dielectric.  The  quantity 
of  electricity  that  a  condenser  will  hold  is  determined  by  the 
capacity  of  the  condenser  and  by  the  pressure  applied. 

A  better  understanding  of  the  action  of  a  condenser  may  be 
had  by  considering  an  analogy.  Suppose  we  have  an  air  tank 
that  under  one  atmospheric  pressure  holds  a  certain  definite 
quantity  of  air,  say  5  Ib.  We  can  define  the  capacity  of  the 
vessel  in  terms  of  the  number  of  pounds  of  air  it  holds,  and  call 
it  a  5-lb.  tank. 


FLOW  OF  CURRENT  IN  A  CIRCUIT  149 

If  the  pressure  is  doubled,  the  tank  will  hold  10  Ib.  of  air. 
Since  we  have  defined  the  capacity  of  the  tank  in  terms  of 
unit  (one  atmosphere)  pressure,  we  cannot  call  it  a  10-lb.  tank. 
A  10-lb.  tank  under  the  same  conditions  will  hold  20  Ib.  of  air. 

Furthermore,  suppose  the  tank  to  be  exhausted;  evidently 
no  back  pressure  will  be  exerted  when  air  is  first  admitted  to  the 
tank.  As  soon  as  some  air  is  admitted  to  the  tank,  back  pressure 
begins  to  manifest  itself,  and  when  the  back  pressure  equals  the 
applied  pressure,  no  more  air  enters  the  tank.  We  thus  see  that 
the  amount  of  air  entering  per  unit  time  depends  upon  the  back 
pressure,  and  this  back  pressure  will  depend  upon  the  capacity 
of  the  tank.  For  instance, 
if  we  put  5  Ib.  of  air  in  a 
10-lb.  tank,  the  back  pressure 
will  be  one-half  as  great  as 
when  5  Ib.  of  air  are  put  into 

a  5-lb.  tank.     We   can  then  l^lxxNw'xx'vM'-'^077  conductor 

say  that  unit   capacity  of  a 
tank  is  such  that  when  1  Ib. 
of   air  is  forced   into   it   the  Conductor 
pressure  will  be  equal  to  one  FIG.  92. 

atmosphere.    Evidently  a  cer- 
tain amount  of  work  will  be  done  in  forcing  the  air  into  the 
tank,  and  we  could  define  unit  capacity  in  terms  of  the  work 
expended. 

The  capacity  of  electrical  conductors  is  analogous  to  the 
capacity  of  the  air  tank  discussed  above.  The  capacity  of  a 
condenser  or  system  of  conductors  is  usually  defined  in  terms  of 
the  quantity  of  electricity  required  to  raise  the  difference  of 
pressure  between  the  terminals  by  one  volt.  In  accordance  with 
this  definition  the  quantity  of  electricity  that  a  condenser  will 
contain  is  equal  to  the  product  of  the  capacity  and  pressure. 

In  so  far  as  determining  current  flow  is  concerned,  the  effect 
of  capacity  in  direct-current  circuits  is  either  negligible  or  it 
serves  as  an  open  circuit.  It  is,  however,  of  considerable  impor- 
tance in  determining  the  flow  of  alternating  currents. 

143.  Resistances  in  Series. — When  resistances  are  connected 
end  to  end,  so  that  the  total  current  must  flow  through  all  of  the 
resistances,  we  say  that  they  are  connected  in  series.  The  total 
assistance  of  several  resistances  so  connected  is  equal  to  the 
sum  of  their  resistances.  This  is  almost  self  evident  and  can  be 


150  MAGNETISM  AND  ELECTRICITY 

easily  understood  by  referring  to  experiment  27,  where  it  was 
shown  that  the  resistance  offered  by  coils  1  and  4  in  series  is 
three  times  that  offered  by  coil  4  only.  Experiment  27,  how- 
ever, is  intended  to  show  how  the  resistance  of  a  conductor  varies 
with  length.  The  same  principles  hold,  however,  when  two  coils 
of  different  lengths,  cross-sectional  areas,  and  materials  are  con- 
nected in  series.  To  show  this,  let  the  student  perform  the  follow- 
ing experiment. 

144.  Experiment  32.     To  Study  Resistances  in  Series. 

Apparatus.  — 
Dry  cells 
Resistance  board 
Volt-ammeter 
Connectors 

Operation.  —  Connect  two  dry  cells,  resistance  board,  and 
volt-ammeter  as  in  Fig.  91.  Adjust  the  resistance  board  so 
that  the  current  must  pass  through  coil  3  only.  Determine 
this  current  and  pressure  across  the  coil  just  as  in  experiment  31. 
Keep  the  circuit  closed  for  an  instant  only  to  prevent  the  burning 
out  of  the  coil.  Take  three  separate  readings  and  average  them. 
Calculate  the  resistance  of  coil  3  by  Ohm's  law;  viz., 


Next  connect  the  board  so  that  the  current  must  flow  through 
coil  4  only  and  measure  the  pressure  and  current  three  times. 
From  the  average  of  the  readings  calculate  the  resistance  of 
coil  4  as  above.  Put  three  dry  cells  in  place  of  the  two  cells 
and  connect  coils  3  and  4  in  series.  To  do  this  the  connections 
shown  in  Fig.  91  will  have  to  be  changed  as  follows:  Transfer 
the  connection  from  binding  post  3  to  binding  post  1  and  also 
transfer  the  wires  from  binding  post  4  to  binding  post  3.  Remove 
plugs  2,  4,  and  7.  The  current  will  then  enter  binding  post  1, 
pass  through  plugs  1,  3,  5,  6,  coil  3,  plug  12,  coil  4,  plug  8  and 
back  to  circuit  through  binding  post  3.  With  this  connection 
measure  the  current  through  coils  3  and  4.  Take  three  or  more 
readings  and  calculate  the  resistance  as  before.  How  does  this 
value  agree  with  the  sum  of  the  resistances  of  coils  3  and  4? 
Tabulate  your  results  as  follows: 


FLOW  OF  CURRENT  IN  A  CIRCUIT 


151 


Coil 

Pressure 
E 

Current 

/ 

Resistance 

H 

3 

4 

3  and  4 

EXAMPLES 

1.  A  pressure  of  10  volts  is  connected  in  series  with  three  resistances  of 
1,  4  and  5  ohms,  respectively.     What  is  the  current? 

Solution. — The  total  resistance  is 


then 


R  =  1+4+5  =  10  ohms 
T      E     10 
=      =  ampere 


2.  Four  equal  resistances  are  connected  in  series,  and  a  pressure  of  50  volts 
is  applied,  when  it  is  found  that  5  amperes  are  flowing.     What  is  the 
resistance  of  each  coil  separately? 
Solution.  —  Total  resistance 


jji         K  A 

R  =  -y-  =  ~F 
/       5 


10  ohms 


Since  10  ohms  is  the  sum  of  4  equal  resistances,  each  must  equal 
1/4  of  10=2.5  ohms  respectively 

3.  A  shunt  generator  field  has  a  resistance  of  50  ohms.     There  is  connected 
in  series  with  the  field  a  regulating  rheostat  whose  resistance  can  be  varied 
from  0  to  40  ohms.     What  is  the  possible  range  of  current  through  the  field 
if  the  pressure  is  110  volts? 
Solution.  —  When  rheostat  resistance  is  0,  the  current  is 

/i  =~KQ~  =2.2  amperes 

When  rheostat  is  all  in,  the  resistance  in  series  is 
50+40  =  90  ohms 


and  current  is 


amperes 


Hence  the  current  can  be  varied  from  if  amperes  to  2.2  amperes. 

E 
145.  Voltage  Drop. — From  the  relation  /  =  ^  we  can  also  get 

lXR  =  E.     That  is,  when  a  current  is  passing  through  a  resist- 


152  MAGNETISM  AND  ELECTRICITY 

ance  the  fall  of  pressure,  or  the  voltage  drop,  is  equal  to  the  prod- 
uct of  current  and  resistance.  For  example,  a  current  of  5 
amperes  flowing  through  a  coil  of  10  ohms  resistance  gives  a 
pressure  drop,  or  voltage  drop,  of  5X10  =  50  volts.  This  princi- 
ple has  already  been  used. 

146.  Experiment  33.  To  Show  That  Voltage  Drop  Equals 
Product  of  Current  by  Resistance. 

Apparatus. — Same  as  in  experiment  32. 

Operation. — Connect  three  dry  cells,  switch,  and  resistance 
board  in  series.  Connect  one  side  of  the  cell  circuit  to  binding 
post  1  and  the  other  to  binding  post  4,  Fig.  85.  Remove  plugs 
3,  4,  and  12.  When  this  is  done  coils  1,  3,  and  4  are  in  series. 
Connect  two  wires  to  the  voltmeter,  that  is,  connect  one  wire  to 
+  and  the  other  to  V  binding  posts,  and  leave  the  other  two  ends 
of  the  wires  free.  Close  the  switch  and  press  the  free  end  of 
one  wire  to  the  brass  block  between  plugs  1  and  3,  and  the  free 
end  of  other  wire  to  the  brass  block  between  binding  posts  9 
and  10.  Observe  the  indication  of  the  voltmeter  and  record  the 
same.  If  the  pointer  deflects  in  the  wrong  direction  interchange 
the  ends.  Next  press  the  free  ends  of  the  wires  connected  to 
voltmeter  on  the  brass  blocks  connected  to  coil  3  and  take  a 
reading.  Finally  press  them  down  upon  the  brass  blocks  con- 
nected to  coil  4.  Repeat  the  readings  so  as  to  be  certain  that 
no  mistake  has  been  made.  Open  the  switch  between  readings 
so  that  the  coils  will  not  heat  up.  Having  determined  the  volt- 
age drop  across  each  coil,  connect  the  cells,  switch/  board,  and 
ammeter  in  series,  as  shown  in  Fig.  86.  The  circuit  wires  must 
be  connected  to  binding  posts  1  and  4  instead  of  1  and  2,  as 
shown  in  Fig.  86.  Remove  plugs  3,  4,  and  12;  close  the  switch 
and  press  down  the  pearl  push-button  on  the  ammeter.  Read 
the  ammeter,  open  the  switch  for  an  instant,  and  close  it  again. 
Take  three  readings  of  the  current.  Tabulate  your  results  as 
follows : 


FLOW  OF  CURRENT  IN  A  CIRCUIT 


153 


Reading 

Coil 

R 

Resistance 

/ 

Current 

IXR 

Voltage  drop 

Difference 

1 

1 

2 

1 

3 

1 

1 

3 

2 

3 

3 

3 

1 

4 

2 

4 

3 

4 

In  column  R  write  the  resistance  of  the  coils  as  determined 
in  experiments  31  and  32,  and  in  column  7  write  the  current  flow- 
ing through  all  three  coils  1,  3,  and  4  in  series.  In  column  IXR 
write  the  products  obtained  by  multiplying  the  current  in  the 
coil  by  its  resistance,  and  in  the  column  marked  voltage  drop, 
write  the  separate  voltmeter  readings  obtained  when  voltmeter 
terminals  were  connected  to,  or  pressed  upon,  the  brass  blocks 
connected  to  coils  1,  3,  and  4  respectively.  How  do  the  products 
IXR  compare  with  the  measured  voltage  drop? 

147.  Theory. — The  subject  of  voltage  drop  is  extremely  im- 
portant in  all  wiring  calculations  and  power  transmission  prob- 
lems. For  instance,  suppose  current  is  sent  over  a  long  trans- 
mission line,  much,  or  several  per  cent,  of  the  voltage  will  be 
necessary  to  overcome  the  resistance  of  the  line.  Suppose  a 
line  of  No.  00  wire  is  5  miles  long  and  20  amperes  are  flowing. 
The  voltage  loss  or  drop  is  equal  to  20  times  the  resistance  of  10 
miles  of  No.  00  wire.  No.  00  wire  has  a  resistance  of  0.0795 
ohms  per  1,000  ft.  at  a  temperature  of  68°  F.  See  Table  VII. 
Ten  miles  is  equal  to  10  X  5,280  ft.  The  resistance  of  this  length 
of  wire  is  52.8X0.0795  =  4.2  ohms.  The  voltage  drop  due  to  20 
amperes  is  4.2  X  20  =  84  volts. 


154 


MAGNETISM  AND  ELECTRICITY 


In  house  wiring,  if  the  resistance  of  the  wires  is  too  high,  the 
voltage  drop  to  the  lamps  will  be  excessive  and  the  lamps  will 
burn  dimly.  The  light-producing  power  of  a  lamp  decreases 
rapidly  with  decrease  of  the  applied  voltage.  A  decrease  of 
5  per  cent  in  the  voltage  may  cause  a  decrease  of  25  per  cent  in 
the  light. 


-AAAAAAvA 

A 

—  AAAA  A  A 

B 

—  A/X  A  A  .A 

V  V  V  V 

\\c 

FIG.  93. 

148.  Resistances  in  Parallel. — The  next  question  we  shall 
investigate  is  the  relation  between  current,  pressure,  and  resist- 
ance, when  several  conductors  are  connected  in  parallel,  that 
is,  connected  as  indicated  in  Fig.  93,  where  R\  and  Rz  represent 
the  several  resistances.  The  student  will  readily  see  that  in  a 
circuit  represented  by  Fig.  93a  the  current  divides  at  the  point 
A,  part  going  through  Ri,  part  through  R2.  The  two  parts  of 


FIG.  93a. 

the  current  combine  again  at  E  from  which  they  flow  as  one 
current.  The  problem  that  we  are  to  solve  is  then  to  determine 
the  total  current  that  will  flow  through  this  circuit  if  we  know  the 
numerical  values  of  Ri,  R^  and  the  pressure  of  the  cell. 

It  is  very  evident  that  if  we  neglect  the  internal  resistance  of 
the  cell  and  the  resistance  of  the  wires  connecting  cell  C  with 


FLOW  OF  CURRENT  IN  A  CIRCUIT  155 

points  A  and  B,  the  difference  of  pressure  between  points  A 
and  B  is  the  pressure  of  the  cell.  This  being  the  case,  the  current 
in  each  conductor  is  given  by  Ohm's  law.  Thus  if  Ji  and  72 
are  the  currents  in  branches  R i  and  R2}  the  currents  are  given  by 

T  -E 
7l~^ 

T        E 

and  1 2  =  w~ 

Kz 

and  the  total  current  must  be  the  sum  of  these  currents.     That  is, 

E      E 


EXAMPLES 

1.  Two  conductors  whose  resistances  are  2  and  3  ohms  respectively  are 
connected  in  parallel  to  a  12-volt  pressure.     What  is  the  total  current? 
What  is  the  joint  resistance? 

Solution. — According  to  what  has  just  been  said,  the  currents  through 
the  separate  resistances  are 

_      E      12 

/i  =  p-  =~2  =  6  amperes 

E      12 

and  /2  =  i^=~o  =4  amperes 

Kz      o 

The  total  current  is  then 

1 1 +/2  =  6+4  =  10  amperes 

We  have  defined  the  resistance  as  the  ratio  of  the  pressure  to  the  current, 
and  accordingly  in  the  example,  when  12  volts  are  applied,  and 
amperes  flow  through  the  circuit,  the  resistance  must  be 

E     12 
/£  =  jr=yQ  =  1.2  ohms 

This  plainly  is  a  quantity  that  differs  from  either  2  or  3  or  their  sum,  5. 

2.  Two  incandescent  lamps  are  connected  in  parallel  across  a  110-volt 
circuit.     One  lamp  has  a  resistance  of  220  ohms  and  the  other  only  110 
ohms.     What  is  the  total  current,  and  what  is  the  joint  resistance? 

Solution. — 

T       110     n* 
1  =  220  =       amPere 

/2  =  110  =  1  amPere 

Total  current  7  =0.5+1  =1.5  amperes 
R  =  110  -r- 1 .5       =  73.67  ohms 


156  MAGNETISM  AND  ELECTRICITY 

149.  Experiment  34.    To  Study  the  Resistance  of  Conductors 
in  Parallel. 

Apparatus. — 

Volt-ammeter 

Two  dry  cells 

Resistance  board 

Connectors 

Switch 

Operation. — Connect  the  two  dry  cells,  volt-ammeter  and 
resistance  board  as  indicated  in  Fig.  91,  measure  the  resistance 
of  coils  3  and  4  separately  according  to  the  directions  of  experi- 
ment 32.  Then  with  plug  11  removed  and  plugs  6,  7,  8,  and  12 
inserted,  measure  the  current  by  pressing  down  on  push-button 
P.  Release  P  and  close  switch  S.  This  gives  the  voltage  drop 
across  coils  3  and  4  in  parallel.  Calculate  the  resistance  by 
Ohm's  law.  How  does  the  current  through  both  coils  compare 
with  the  sum  of  the  currents  through  the  separate  coils? 

150.  Theory. — The  foregoing  experiment  shows  clearly  that 
when  two  resistances  are  connected  in  parallel,  the  total  current 
is  equal  to  the  sum  of  the  currents  in  each  conductor.     The 
student  may  not  be  able  to  get  values  that  show  this  with  mathe- 
matical exactness.     The  reason  for  this  is  evident;  the  resistances 
of  the  connecting  wires  and  cells  modify  this  condition  to  some 
extent.     These  external  resistances  are  a  greater  per  cent  or 
part  of  the  joint  resistance  of  spools  1  and  3  than  of  the  resistance 
of  either  spool  alone.     The  current  in  every  case  is  determined 
by  the  resistance  of  cells,  connecting  wires,  and  spools.     If  the 
resistance  of  the  cells  and  wires  is  a  greater  percentage  of  the 
joint  resistance  than  of  the  resistance  of  either  spool,  the  current 
through  the  spools  in  parallel  must  be  somewhat  less  than  the 
sum  of  the  currents  obtained  when  the  spools  are  connected  to 
the  cells  separately.    This  external  resistance  is  so  small  that 
the  values  are  close  enough  for  practical  purposes. 

A  water  pipe  analogy  may  help  to  make  the  foregoing  principles 
clear.  If  two  equal  pipes  are  connected  side  by  side,  each  will 
carry  the  same  water  current  and  the  total  current  is  the  sum 
of  the  currents  in  the  two  pipes.  Also  this  total  current  is  two 
times  the  current  carried  by  one  pipe  when  the  pipes  are  exactly 
alike  in  every  respect.  The  same  principle  holds  in  electrical 
conductors.  The  current  through  two  conductors  of  equal 
resistances  in  parallel  is  two  times  the  current  in  one  conductor, 


FLOW  OF  CURRENT  IN  A  CIRCUIT  157 

and  accordingly  the  resistance  must  be  equal  to  half  of  that 
offered  by  one  conductor.  This  can  be  looked  upon  from  still 
another  viewpoint.  When  two  conductors  of  the  same  size 
are  connected  in  parallel,  the  cross-sectional  area  of  the  two 
conductors  is  evidently  equal  to  twice  that  of  one.  Then  if  the 
resistance  of  one  is  given  by 

^1=  T  (see  Pa8e  135) 
the  resistance  of  two  in  parallel  will  be  given  by 


since  the  only  quantity  that  has  been  changed  is  A,  the  cross- 
sectional  area.     Ri  +  Rz  is  thus 


2A 

That  is,  the  resistance  of  one  is  twice  the  joint  resistance  of  the 
two  conductors  in  parallel. 

151.  Calculation  of  Joint  Resistance.  —  When  the  wires  are 
connected  in  parallel  the  joint  resistance  can  be  determined 
experimentally  as  in  the  foregoing  experiment.  The  facilities 
for  thus  determining  the  resistance  are  not  always  available; 
hence,  in  most  instances  it  is  preferable  to  calculate  the  joint 
resistance.  This  can  be  done  readily  when  the  principles  are 
understood. 

It  has  been  shown  that  when  two  resistances,  R\  and  Ri,  are 
connected  in  parallel  to  a  pressure  E,  the  total  current  is  given 

by 


/= 


This  means  that  7,  the  total  current,  is  equal  to  E,  the  pressure, 
multiplied  by  the  sum  of  the  reciprocals  of  the  two  resistances. 
(The  reciprocal  of  any  number  is  one  divided  by  the  number.) 


158  MAGNETISM  AND  ELECTRICITY 

If  R  is  the  joint  resistance,  the  current  by  Ohm's  law  is  given  by 


Then  -p-  must  equal  E  (jr+  rr 


r—  =  E  (—    — 

R       \RI   R2 


Cancelling  the  E's,  we  get 


-=-+- 

R     RI    R 


J  _ 
R- 

Taking  the  reciprocal  of  both  sides  of  the  equation,  this  becomes 


or       . 


That  is,  the  joint  resistance  of  two  resistances  in  parallel  is 
equal  to  the  product  of  the  resistances  divided  by  their  sum. 

EXAMPLE 

Two  wires  whose  resistances  are  2  and  3  ohms  are  joined  in  parallel. 
What  is  the  joint  resistance? 

Solution. — Joint  resistance  is  given  by 

p.  v  P. 
R 


#2=3 

o-y  O 

Then  #  =          =  1.2  ohms 


Compare  this  value  with  that  obtained  in  the  illustrative  example  on 
page  155. 

When  the  two  wires  are  exactly  alike,  or  have  equal  resistances,  Ri=R2 
and  our  formula  reduces  to 


P  _  RI*     RI 

" 


That  is,  the  joint  resistance  is  equal  to  half  the  resistance  of  one  conductor. 


FLOW  OF  CURRENT  IN  A  CIRCUIT  159 

152.  Three  or  More  Conductors  in  Parallel. — The  same  general 
principles  apply  when  three  or  more  conductors  are  connected 
in  parallel.  For  three  conductors  whose  separate  resistances 
are  jRi,  R%,  and  Rs,  Fig.  93a,  the  joint  resistance  may  be  calculated 
by  the  following  relation: 

.        E      E      E 


=  E 

Tjl 

=  ip?  where  R  is  the  joint  resistance,  and 

w 
hence,  D  =#  (ir+Tr+rr 


-_--. 

R       RI      RZ      Rs 


7?  7?    7?    7? 

Whence  by  taking  reciprocals,  we  again  get, 

7?  7?  7? 

R  = 


which  means  that  the  joint  resistance  of  three  conductors  is 
equal  to  the  product  of  the  resistances  divided  by  the  sum  of 
the  products  obtained  by  multiplying  together  two  of  the  resist- 
ances at  a  time. 

EXAMPLE 

Find  the  joint  resistance  of  3  conductors  whose  separate  resistances  are 
2,  3,  and  4  ohms  respectively. 

Solution. — 


Then   R  = 


Ri=2  ohms,  #2=3  ohms,  -R3=4  ohms 
2X3X4 


2X3+2X4+3X4 

24          24     12    , 

,=^77=T7r  ohms 


6+8  +  12     26     13 

In  general,  we  can  calculate  the  joint  resistance  of  any  num- 
ber of  conductors  connected  in  parallel  in  exactly  the  same  way. 
It  is  not  necessary  to  show  how  any  more  formulas  are  calcu- 
lated. A  general  rule  will  suffice.  To  find  the  joint  resistance 

16 


160  MAGNETISM  AND  ELECTRICITY 

of  any  number  of  parallel  resistances,  divide  the  product  of  all  of 
the  resistances  by  the  sum  of  the  products  obtained  by  multiplying 
together  all  of  the  resistances  less  one.  The  same  resistance  must 
not  appear  in  any  one  product  more  than  once. 

EXAMPLE 

Find  the  joint  resistance  of  five  resistances  R\,  R2,  Rs,  #4,  and  R&. 

Solution. — The  product  of  the  resistances  is  Ri XR^XRsXR* XR&.  Since 
there  are  5  resistances,  the  divisor  must  contain  the  products  obtained  by 
taking  four  resistances  at  a  time.  The  only  possible  products  we  can  make, 
using  each  resistance  only  once  in  each  product,  are 


product  of  five  resistances 
"sum  of  products  taken  4  at  a  time 
Suppose  #i=2,  #2  =  3,  #3  =  4,  #4  =  5,  and  #6  =  10 
Then        #:X#2X#3X#4X#6  =  2X3X4X5X10  =  1200 


#2  X#3  X  #4  X#5  =  600 

Sum  1660 

,          1200     60 
and  #=          =       ohms 


153.  Practical    Applications.  —  Parallel    conductors    are    used 
extensively  in  practice.     All  cables  and  flexible  conductors  are 


GENERATOR    f]          O  O  O  O  LAMPS 


•o- 
-o- 

o 


FIG.  94. 


in  reality  a  bundle  of  parallel  wires.  In  alternating  current 
power  transmission,  it  is  often  preferable  to  use  stranded  con- 
ductors in  preference  to  solid  conductors.  Incandescent  lamps 
are  almost  always  connected  in  parallel  as  indicated  in  Fig.  94. 


FLOW  OF  CURRENT  IN  A  CIRCUIT  161 


FIG.  95. 


•X9//7 


FIG.  96. 


'.-•Res/stance 
wire 


162 


MAGNETISM  AND  ELECTRICITY 


The  resistance  of  the  lamps  thus  decreases  with  the  increase  in 
the  number  of  lamps. 


FIG. 


Nearly  all  current-controlling  apparatus  consists  of  merely 
a  combination  of  wires  or  metal  in  some  form  whose  resistance  is 
effective  in  regulating  the  current.  Thus  motor  starters  and  field 


FIG.  99. 


resistances  are  rheostats  whose  resistance  may  be  varied.  One 
type  of  field  rheostat  is  shown  in  Fig.  95.  These  field  rheostats 
consist  of  a  circular  base  plate  of  insulating  material  to  which  is 


FLOW  .OF  CURRENT  IN  A  CIRCUIT 


163 


%7/7/rs  ir?  Ser/f>3  - 


FlG.   100. 

attached  the  resistance  wire,  con- 
tacts and  lever,  the  whole  being 
enclosed  in  a  ventilated,  j  apanned 
iron  case  of  attractive  design.  A 
cross-section  of  the  rheostat 
showing  the  construction  is 
shown  in  Fig.  96.  The  manner 
in  which  the  resistance  of  this 
type  of  field  rheostat  is  increased 
or  decreased  will  be  understood 
from  Fig.  97. 

For  motor  starting  the  rheo- 
stats are  also  made  in  many  dif- 
ferent forms.  One  form  for 
mounting  on  the  wall  or  a  panel 
board  is  shown  in  Fig.  98.  The 
type  of  resistance  used  is  shown 
in  Fig.  99.  For  the  control  of 
series  street  railway  motors  the 
resistances  are  usually  made  in 
the  form  of  grids  shown  in  Fig. 
100. 

154.  Cells  in  Series.— Al- 
though in  most  of  the  experiments 

discussed  so  far  two  or  more  cells  in  series  have  been  employed, 
the  principles  that  govern  such  a  connection  have  not  been  ex- 
plained. In  the  discussion  of  Ohm's  law  it  was  stated  that  E, 


GLT 


FIG.  101. 


164 


MAGNETISM  AND  ELECTRICITY 


the  pressure,  must  be  the  total  electromotive  force  in  the  circuit. 
What  is  the  total  electromotive  force  when  cells  are  connected 
in  series  as  shown  in  Fig.  101?  The  analogous  diagram  of 
tanks  in  series  may  help  to  make  this  clear.  The  hydrostatic 
pressure  at  A  is  evidently  the  sum  of  the  pressures  due  to  the 
elevations  of  the  water  AB-\-BC-\-CD.  That  is,  it  is  the  sum 
of  the  pressures  of  the  separate  tanks.  Similarly,  the  electrical 
pressure  between  the  terminals  1  and  2  is  the  sum  of  the  pres- 
sures across  cells  a,  b,  and  c. 

155.  Experiment  35.     To  Study  the  Pressure  of  Cells  in  Series. 
Apparatus. — 
Volt-ammeter. 
Three  dry  cells. 

Operation. — The  manner  of  connecting  the  volt-ammeter  to 
the  cells  has  been  explained  in  detail  so  many  times  that  here- 
after detailed  explanations  will  be  omitted. 

Take  three  dry  cells  and  measure  the  voltage  of  each  sepa- 
rately. Record  these  thus: 

VOLTAGE  OF  CELLS 


Cell  (a) 

Cell  (b) 

Cell  (c) 

Total 

1 

1.40 

1.45 

1.35 

4.20 

2 

3 

4 

Mean 

Then  connect  two  cells  in  series  and  measure  the  voltage  across 
both.  Compare  the  voltmeter  registration  with  the  sum  of  the 
voltages  of  the  two  cells.  Next  connect  the  three  cells  in  series 
exactly  as  indicated  in  Fig.  101  and  measure  the  voltage  across 
all  three  cells.  Compare  this  value  with  the  sum  of  the  three 
voltages.  Does  the  experiment  show  that  the  total  voltage  of 
cells  in  series  is  equal  to  the  sum  of  the  several  voltages? 

Reverse  the  connection  of  one  of  the  cells  and  again  measure 
the  total  voltage.  Is  it  the  same  as  before?  Why? 

156.  Theory. — When  cells  are  connected  so  that  the  pressure 
of  each  is  in  the  same  direction,  the  total  pressure  is  equal  to  the 
sum  of  the  several  pressures.  In  general,  if  E  is  the  pressure  of 
one  cell  and  n  cells  are  connected  in  series,  the  total  pressure  is 
nE. 


FLOW  OF  CURRENT  IN  A  CIRCUIT 


165 


J 


AJ 


EXAMPLE 

What  is  the  total  pressure  when  5  Daniell  or  gravity  cells  are  connected 
in  series? 

Solution. — The  pressure  of  one  gravity  cell  is  approximately  1.1  volts; 
hence  of  five  cells  in  series  the  pressure  is  5X1.1  =5.5  volts. 

157.  Battery  Resistance  for  Series  Connections. — It  must  be 
noted  that  as  each  cell  connected  has  some  internal  resistance, 
connecting  cells  in  series  is  the 

same  as  connecting  wires  in 
series.  That  is,  the  resistance 
of  the  battery  is  the  sum  of 
the  resistances  of  the  separate 
cells.  If  r  represents  the  in- 
ternal resistance  of  one  cell, 
the  resistance  of  a  battery  of 
n  cells  is  nr. 

158.  Cells  in  Parallel.— Fig. 
102  is  a  diagram  of  tanks  and 
cells  connected  in.parallel.     It 
is  evident  that  the  hydrostatic 
pressure  exerted  by  the  water 
in  tank  A  is  the  same  as  that 
in  B  and  C,  since  the  height 
of  the  water  is  the  same  in 
each.     The  total  pressure  is 
equal   to   that   of   one   tank. 

The  three  tanks  could  be  replaced  by  one  large  tank,  and  as 
long  as  the  water  was  maintained  at  the  same  height,  the  pres- 
sure at  the  orifice  would  be  exactly  the  same  in  the  two  cases. 

When  cells  are  connected  in  parallel  the  total  pressure  is  equal 
to  the  pressure  of  one  cell,  and  the  three  cells  a,  b,  and  c  can  be 
replaced  by  one  large  cell  having  the  same  cross-section  of  zinc 
and  carbon  as  the  three  cells  taken  together. 

When  tanks  are  connected  in  parallel  it  is  evident  that  each 
supplies  only  a  part  of  the  current.  The  same  principle  holds 
with  reference  to  cells  connected  in  parallel — each  cell  supplies 
only  a  part  of  the  total  current.  The  student  can  readily  verify 
the  law  of  pressures  by  connecting  three  cells  in  parallel  and  then 
connecting  the  voltmeter  to  terminals  1  and  2,  Fig.  102,  and 
comparing  the  voltmeter  reading  with  the  reading  given  when 
the  voltmeter  is  connected  to  each  cell  separately. 


FIG.  102. 


166 


MAGNETISM  AND  ELECTRICITY 


159.  Battery  Resistance  for  Parallel  Connections. — The  effect 
of  connecting  cells  in  parallel  is  to  increase  the  current  capacity 
and  decrease  the  internal  resistance.     In  so  far  as  the  internal 
resistance  of  one  cell  is  concerned,  it  may  be  considered  as  a 
conductor  whose  resistance  is  r.     Three  cells  in  parallel  will 
thus  be  the  equivalent  of  three  resistances  in  parallel.     It  has 
been  shown  that  when  three  equal  resistances  are  in  parallel, 
the  joint  resistance  is  equal  to  one-third  of  the  resistance  of  one 
wire.     Accordingly,  the  joint  internal  resistance  of  a  battery  of 

m  parallel  cells  is  — . 

EXAMPLE 

Five  cells  each  having  an  internal  resistance  of  1  ohm  are  connected  in 
parallel.  What  is  the  joint  resistance? 

Solution. — Since  the  resistances  of  the  cells  are  the  same,  the  joint  resist- 
ance is  1/5  of  1  ohm  =  0.2  ohm. 

160.  Series   Parallel   Connection. — In   some   instances   it   is 
advisable  to  connect  several  series  groups  in  parallel;  such  a 


FIG.  103. 

connection  is  shown  in  Fig.  103.  The  total  pressure  between 
terminals  1  and  2  is  equal  to  the  pressure  of  one  series  group. 
The  internal  resistance  of  such  an  arrangement  is  equal  to  the 
resistance  of  the  cells  in  series  divided  by  the  number  of  groups 
connected  in  parallel.  Using  the  same  notation  as  before,  if  r 
represents  the  resistance  of  one  cell,  the  internal  resistance  of  n 
cells  in  series  is  nr  ohms.  If,  now,  m  series  groups  are  connected 

in  parallel,  the  joint  resistance  is  —  ohms. 


FLOW  OF  CURRENT  IN  A  CIRCUIT 


167 


EXAMPLE 

If  the  internal  resistance  of  each  cell  is  2  ohms,  what  is  the  battery  resist- 
ance of  Fig.  103? 

Solution. — There  are  three  cells  in  series  and  five  series  groups  in  parallel; 
hence  the  joint  resistance  is 

nr     3X2       - 
H=      = — ~ —  =  1-t  ohms 
m       o 

161.  Ohm's  Law  as  Applied  to  Cells  in  Series  and  Parallel. — 

It  has  been  mentioned  several  times  that  in  determining  the 
current  by  Ohm's  law  it  is  necessary  to  take  into  consideration 
the  internal  or  battery  resistance.  When  cells  are  connected 
in  series  only,  this  internal  resistance  is  nr,  and  the  pressure  is 


FIG.  104. 


FlG.    105. 


nE,  where  E  is  the  pressure  of  one  cell.     If  R  represents  the 
external  resistance  then  by  Ohm's  law  the  current  is 

nE 
R+nr 

Such  a  connection  is  shown  in  Fig.  104. 

The  current  given  by  a  parallel  connection  can  be  calculated 
in  the  same  way.     The  total  pressure  is  equal  to  that  of  one  cell, 

and  as  the  internal  resistance  is  — ,  the  current  in  a  circuit  whose 

external  resistance  is  R  is 

E 


m 


A  diagram  of  such  a  connection  is  shown  in  Fig.  105. 

If  cells  are  connected  in  series-parallel  as  shown  in  Fig.  103, 

nE 
the  current  through  an  external  resistance  R  is  then 


168  MAGNETISM  AND  ELECTRICITY 

EXAMPLE 

What  current  will  flow  through  a  2-ohm  coil  connected  to  terminals  1  and 
2,  Fig.  103,  if  each  cell  has  a  pressure  of  1.4  volts  and  an  internal  resistance 
of  1  ohm? 


Solution.  — 

E 

=  1, 

4 

n 

=  3 

r 

=  1 

in 

=  5 

R 

=  2 

Then 

I 

nE          3X1.4 

£ 

nr-  2    ,3X1 

f-T~         •    T  r 

$-  =  ~-^  =  1.6  amperes,  nearly. 
6       2.0 


162.  Best  Grouping  of  Cells.  —  Whether  a  certain  grouping 
of  cells  is  better  than  another  will  depend  upon  the  conditions 
of  service.  If  cells  are  to  be  used  in  such  a  way  as  to  have  a  long 
life,  that  is,  if  they  are  to  have  a  long  life  and  comparatively 
high  efficiency,  the  parallel  grouping  is  preferable.  When  such 
a  grouping  is  used,  the  materials  of  the  cells  will  be  consumed 
slowly,  and  there  will  be  a  minimum  waste  of  energy. 

If  it  is  desired  to  obtain  the  greatest  possible  current  from  a 
given  number  of  cells,  and  the  cells  are  to  be  grouped  in  series- 
parallel  only,  the  best  manner  of  grouping  them  will  be  such  as 
to  make  the  internal  resistance  of  the  battery  equal  to  the  external 
resistance.  Although  this  arrangement  gives  the  strongest 
current,  it  is  not  the  most  efficient;  for,  if  the  internal  and  external 
resistances  be  equal  to  one  another,  the  useful  work  in  the  external 
part  of  the  circuit  is  only  half  the  total  energy.  The  other  half 
of  the  energy  is  wasted  inside  of  the  cells. 

EXAMPLE 

Given  six  cells  each  having  2  volts  pressure  and  2  ohms  internal  resistance, 
how  should  the  cells  be  connected  to  give  the  greatest  current  through  a  3- 
ohm  coil? 

Solution.  —  In  order  that  the  current  may  be  a  maximum,  the  internal 
resistance  must  equal  the  external  resistance. 

Let     n   =  number  cells  connected  in  series 

m  =  parallel  groups 
then  nXm  =6 

*«  vy  O 

The  internal  resistance  is  -  »   but  this  must  equal  3  ohms. 


FLOW  OF  CURRENT  IN  A  CIRCUIT  169 


2n    =3m 
But          m  —- 

3X6 
then         2n  =  - 


n2   =9 

n     =  \r  9  =  3  =  number  of  cells  in  series 

/> 

m  =o  =2  parallel  groups 

When  such  a  connection  is  made,  the  current  is 

/=3_X2_     =6  =  lampere 
3+3|2 

No  other  grouping  of  the  cells  will  give  any  greater  current.  For  instance, 
if  the  cells  had  been  connected  two  cells  in  series  and  in  3  parallel  groups, 
the  current  would  have  been 

7_2X2_         4^19 

~3+?^~4*  ~13ai 
o          o 

In  the  discussion  of  electromagnets  it  was  shown  that  self 
induction  prevented  the  sudden  rise  of  current  in  such  a  circuit. 
The  time  during  which  the  circuit  is  closed  also  helps  determine 
the  maximum  current  that  will  flow  through  such  a  circuit.  The 
time  required  for  the  current  in  an  inductive  circuit,  such  as  an 
electromagnet  or  induction  coil,  to  reach  a  certain  per  cent  of  its 
maximum  value  as  indicated  by  Ohm's  law,  is  determined 
by  the  ratio  of  the  inductance  and  resistance.  This  ratio, 

r>,  is  known  as  the  time  constant  and  the  smaller  this  ratio  the  more 

quickly  does  the  current  reach  a  relatively  large  value.  This 
ratio  is  small  when  R  is  large,  and  R  is  large  relatively  when  cells 
are  connected  in  series.  Hence  when  cells  are  used  on  inductive 
circuits,  quick  action  is  secured  by  connecting  the  cells  in  series. 

RECAPITULATION 

1.  According  to  Ohm's  Law  the  current  in  a  circuit  is  directly  propor- 
tional to  the  pressure.  For  direct-current  circuits  it  is  usually  ex- 
pressed thus, 

E 


170  MAGNETISM  AND  ELECTRICITY 

Where  I  is  current  in  amperes,  E  is  the  pressure  in  volts  and  R  is  the 
resistance  in  ohms. 

2.  By  capacity  is  meant  the  property  of  a  conductor  or  a  system  of 
conductors  for  storing  electricity.    The  unit  of  capacity  is  the  farad. 
A  farad  is  that  capacity  which  will  be  charged  to  a  difference  of  one 
volt  by  coulomb;  a  micro-farad  is  one-millionth  of  a  farad. 

3.  When  resistances  are  connected  in  series,  the  joint  resistance  is 
equal  to  the  sum  of  the  resistances  connected. 

4.  By  voltage  drop  is  meant  the  fall  of  electrical  pressure  between  two 
points  on  a  conductor.    It  is  equal  to  the  product  of  the  current  by  the 
resistance  between  the  two  points.    Algebraically  it  may  be  written 


5.  The  joint  conductivity  of  several  resistances  connected  in  parallel  is 
equal  to  the  sum  of  the  separate  conductivities,  and  the  joint  resistance 
of  several  resistances  connected  in  parallel  is  the  reciprocal  of  their  joint 
conductivities.    To  find  the  joint  resistance  of  any  number  of  parallel 
conductors  divide  the  product  of  all  of  the  resistances  by  the  sum  of  the 
products  obtained  by  multiplying  together  all  of  the  resistances  less  one. 
The  same  resistance  must  not  appear  in  any  one  product  more  than  once. 

6.  When  cells  are  connected  in  series  the  total  pressure  is  equal  to  the 
sum  of  the  pressures  of  the  cells.    The  internal  resistance  is  equal  to  the 
sum  of  the  resistances  of  the  several  cells. 

7.  When  cells  are  connected  in  parallel,  the  resulting  pressure  is  the 
pressure  of  one  cell.    The  internal  resistance  is  equal  to  the  resistance 
of  one  cell  divided  by  the  number  of  cells. 

8.  Cells  may  be  grouped  in  series-parallel.    When  so  connected  the 
total  pressure  is  equal  to  the  number  of  cells  in  series.     When  a  series- 
parallel  group  of  cells  is  connected  to  resistance  R,  the  current  is  given 

by 

nE 

" 


Where  E  is  the  pressure  of  one  cell,  n  is  the  number  of  cells  in  series, 
m  is  the  number  of  series  groups  connected  in  parallel  and  r  is  the  in- 
ternal resistance  of  one  cell. 

9.  When  cells  are  to  be  grouped  for  maximum  current  output,  and 
only  the  series-parallel  grouping  is  to  be  employed,  they  are  to  be 
grouped  so  that  the  internal  resistance  equals  the  external  resistance. 


CHAPTER  IX 

INDUCED   CURRENTS  AND   PRINCIPLES   OF  THE   ELECTRIC 
GENERATOR  AND  MOTOR 

163.  Introduction. — Some  of  the  most  elementary  principles 
of  inducing  an  electromotive  force  were  discussed  briefly  in 
Chapter  III.     It  was  there  shown  that  whenever  a  permanent 
magnet  was  inserted  or  removed  quickly  from  a  solenoid  the 
ends  of  which  were  connected  to  a  galvanoscope,  the  compass 
needle  was  deflected.     The  amount  of  the  deflection  was  de- 
termined by  the  rapidity  with  which  the  magnet  was  moved, 
and  the  direction  of  deflection  depended  upon  whether  the  N- 
or  $-pole  was  being  inserted  or  withdrawn.     It  was  also  shown 
that  the  direction  of  the  induced  current  was  in  every  case  such 
that  the  magnetic  field  due  to  the  current  opposed  the  motion 
of  the  bar  magnet.     We  shall  now  investigate  these  principles 
more  fully,  and  learn  how  they  are  applied  in  practice. 

164.  The  Generator. — A  simple  generator  or  motor  is  among 
the  apparatus  sent  the  student.     A  drawing  of  this  is  shown  in 
Fig.    106.     Comparing   this   drawing   with   the   apparatus   the 
student  will  observe  that  C  is  an  iron  core  around  which  have 
been  wound  two  coils  of  insulated  wire.     The  two  free  ends  of 
the  coils  are  connected  to  two  halves  of  a  split  brass  cylinder  on 
the  shaft  by  means  of  two  screws.    The  two  pieces  of  brass  cylin- 
der are  insulated  from  each  other  and  from  the  iron  shaft  by  a 
fiber  cylinder  to  which  the  brass  pieces  are  fastened.     The  iron 
core,  C,  I^ig.  106,  with  its  windings  is  called  the  armature,  and 
the  split  brass  cylinder  is  called  the  commutator.     Both  arma- 
ture and  commutator  are  mounted  on  a  shaft  which  permits  of 
their  rotation. 

Resting  on  opposite  sides  of  the  commutator  are  two  copper 
wires  called  brushes.  These  brushes  are  attached  to  two  holders 
which  in  turn  are  held  in  place  by  two  binding  posts  A  and  B. 
The  electric  circuit  then  begins  at  one  binding  post,  continues 
through  one  brush  holder  and  brush  to  one  commutator  segment, 
then  through  the  winding  on  the  armature  to  the  other  commu- 

18  171 


172 


MAGNETISM  AND  ELECTRICITY 


tator  segment,  through  the  other  brush  and  brush-holder,  and 
back  to  the  other  binding  post. 

Within  two  wooden  blocks  are  two  bar  magnets  M-M'.  These 
are  movable  around  two  screws  at  the  ends  of  the  blocks  as 
centers.  By  means  of  such  a  mounting  the  two  bar  magnets 
can  be  moved  with  reference  to  the  armature. 


yore 

c 


FIG.  106. 

165.  Experiment  36.    To   Study  Principles  of  the  Electric 
Generator. 

Apparatus. — 
Generator  on  board 
Volt-ammeter 

Operation. — Connect  the  volt-ammeter  to  the  binding  posts 
of  the  generator  as  shown  in  Fig.  106.  Wrap  a  string  around 
the  shaft  above  the  commutator  in  the  same  manner  as  a  string 
is  wrapped  around  the  stem  of  a  top  or  gyroscope.  If  a  grooved 
pulley  is  available,  a  better  plan  is  to  make  a  string  belt  and 
pass  it  around  the  grooved  pulley  and  shaft  of  the  armature 
above  the  commutator.  By  turning  the  grooved  pulley  the 
armature  may  be  caused  to  rotate  at  a  high  speed  and  the  speed 
can  also  be  varied  at  will.  The  driving  wheel  of  a  sewing 
machine  may  be  utilized  for  this  purpose. 


INDUCED  CURRENTS 


173 


174  MAGNETISM  AND  ELECTRICITY 

See  that  opposite  poles  of  the  bar  magnets  are  near  the  arma- 
ture; press  down  the  button  on  the  ammeter  and  cause  the 
armature  to  rotate  rapidly  by  pulling  on  the  string,  or  by  turning 
the  driving  wheel.  While  the  armature  is  in  motion  observe 
the  pointer  of  the  ammeter.  Does  it  deflect?  In  which  direc- 
tion? Reverse  the  direction  of  rotation  of  the  armature  and 
again  observe  the  ammeter  pointer.  Does  the  direction  of  the 
deflection  of  the  pointer  depend  upon  the  direction  of  rotation 
of  the  armature?  Turn  the  bar  magnets  end  for  end  and 
repeat.  Does  the  direction  of  the  deflection  depend  upon  the 
polarity  of  the  bar  magnets?  If  possible  maintain  the  speed  of 
rotation  constant  and  observe  whether  the  pointer  remains  nearly 
stationary. 

Can  you  explain  why  the  deflection  of  the  pointer  is  always  in 

one  direction  as  long  as  the  arma- 
ture rotates  in  one  direction?  If 
the  student  will  refer  to  his  results 

"FIG    loTa"  °^  exPeriment  18  he  will  see  that 

the  compass  needle  was  deflected 
in  one  direction  when  the  magnet  was  withdrawn.  What  ac- 
counts for  the  different  behavior  of  the  compass  needle  and 
pointer  of  the  ammeter? 

166.  Theory. — In  experiment  18  the  coil  was  held  stationary 
while  in  this  experiment  the  magnets  are  stationary  and  coils 
are  rotated.  When  the  opposite  poles  of  the  two  bar  magnets 
are  near  the  armature,  the  magnetic  field  extends  from  one  to 
the  other  as  was  demonstrated  by  the  student  in  experiment  5. 
A  diagram  of  this  field  is  shown  in  Fig.  107a.  The  magnetic 
lines  pass  from  the  N-pole  of  one  bar  magnet  through  the  arma- 
ture core  to  the  iS-pole  of  the  other  magnet.  As  the  armature 
rotates  the  winding  cuts  across  these  lines  as  indicated  in  Fig. 
107b.  The  magnetic  lines  enter  the  coil  from  the  side  A  at  first, 
but  when  the  armature  has  made  one-half  of  a  rotation,  the  lines 
enter  from  the  side  B.  During  this  half  rotation  the  direction 
of  the  lines  within  the  core  has  reversed,  and  according  to  the 
principles  of  experiment  18  an  electromotive  force  must  be 
induced  in  the  windings  while  this  relative  motion  takes  place. 
Furthermore,  it  must  be  clear  that  if  the  direction  of  the  mag- 
netic lines  with  reference  to  the  armature  coils  is  reversed  every 
half  rotation  the  induced  electromotive  force  must  be  in  one 
direction  during  one  half  of  the  rotation,  and  in  the  opposite 


INDUCED  CURRENTS  175 

direction  during  the  other  half  of  the  rotation;  and  yet  the 
student  saw  that  the  pointer  of  the  ammeter  was  deflected  in 
only  one  direction.  The  question  is,  how  was  this  accom- 
plished? The  student  perhaps  already  surmises  that  the  com- 
mutator has  something  to  do  with  this. 

An  examination  of  the  apparatus  will  show  that  the  brushes 
rest  on  diametrically  opposite  points  of  the  commutator,  and 
that  at  no  time,  or  for  only  the  briefest  instant  during  the  rota- 
tion of  the  commutator,  do  the  brushes  rest  on  the  same  segment 


BAK  MASNCT 


FIG.  107b. 

of  the  commutator.  As  the  armature  rotates  the  brushes  make 
contact  first  with  one  segment,  and  after  a  half  rotation,  with 
the  other  segment.  Thus  if  the  current  in  the  armature  coil 
is  in  such  a  direction  as  to  come  out  at  the  binding  post  B,  Fig. 
106,  during  the  first  half  rotation,  it  must  also  flow  out  at  the 
same  binding  post  during  the  second  half  of  the  rotation;  for 
where  the  direction  of  current  in  the  armature  coils  is  reversed, 
the  commutator  segments  have  changed  brush  contacts.  The 
commutator  thus  serves  to  reverse  or  exchange  the  connections 


176 


MAGNETISM  AND  ELECTRICITY 


of  the  armature  coil  at  every  half  rotation.  While  the  current 
in  the  armature  coils  reverses  its  direction  of  flow  every  half 
rotation,  that  in  the  external  circuit  flows  continuously  in  one 
direction.  The  purpose  of  the  commutator  is  thus  to  convert 
the  alternating  armature  current  into  a  uni-direction,  or  one 
direction,  current  in  the  external  circuit.  A  direct-current 
generator  armature  with  commutator  is  shown  in  Fig.  108. 

The  electromotive  force  is  induced  in  the  windings  of  the 
armature  in  exactly  the  same  way  as  in  experiment  19.  The 
magnetic  field  is  due  to  the  two  bar  magnets  when  placed  so 
that  opposite  poles  are  near  each  other.  That  unlike  poles 
must  be  adjacent  in  order  that  an  electromotive  force  may  be 
induced  can  be  shown  easily  by  turning  one  of  the  magnets  end 


Commutator 


FIG.  108. 

for  end  and  repeating  the  experiment.     When  this  is  done  it 
will  be  seen  that  no  electromotive  force  is  generated. 

167.  Experiment   37.    To    Study   the   Relation   of   Induced 
Electromotive  Force  to  Speed. 

Apparatus. — Same  as  for  experiment  36. 

Operation. — Connect  the  apparatus  as  before  and  rotate  the 
armature  first  slowly  and  note  the  deflection  of  the  pointer  of 
the  ammeter.  Next  rotate  it  at  a  higher  speed  and  again  note 
the  deflection.  Has  it  increased  or  decreased?  Repeat  once 
more  by  turning  the  armature  at  still  a  higher  speed  and  again 
observe  the  deflection.  Can  you  make  any  deduction  as  to  the 
increase  or  decrease  of  the  electromotive  force  with  speed? 

168.  Theory. — From  the  results  obtained  no  exact  mathe- 
matical relation  between  the  strength  of  the  induced  electromo- 
tive force  and  speed  can  be  given,  for  neither  the  speed  nor  the 


INDUCED  CURRENTS 


177 


pressure  was  measured,  but  even  so  simple  an  experiment 
shows  that  the  higher  the  speed  the  higher  the  electromotive 
force  induced.  The  strength  of  the  magnetic  field  is  kept  con- 
stant, the  number  of  turns  on  the  armature  is  the  same;  hence 
as  the  speed  is  the  only  factor  that  is  changed  we  are  justified 
in  saying  that  the  induced  pressure  depends  upon  the  speed 
of  the  armature,  increasing  as  the  speed  increases  and  decreasing 
as  the  speed  decreases. 


FIG.  109. 


169.  Experiment  38.    To  Study  the  Relation  between  Strength 
of  Magnetic  Field  and  Induced  Electromotive  Force. 

Apparatus. — 
Volt-ammeter 
Generator 
Two  dry  cells 
Electromagnet 

Operation. — First  connect  the  apparatus  as  in  experiment  37. 
Place  the  opposite  poles  of  the  bar  magnets  near  the  armature 


178  MAGNETISM  AND  ELECTRICITY 

and  rotate  the  armature  at  quite  a  high  speed.  Observe  the  de- 
flection. Move  the  bar  magnets  about  half  an  inch  away  from 
the  pegs  in  the  center  of  the  board  and  again  rotate  the  armature 
at  the  same  speed.  How  does  the  deflection  of  the  ammeter 
pointer  compare  with  that  previously  made?  Move  the  bar 
magnets  another  half  inch  and  repeat.  Repeat  this  until  no 
deflection  is  observed. 

Next  swing  the  bar  magnets  entirely  to  one  side  and  place  the 
electromagnet  in  position  as  shown  in  Fig.  109.  Connect  one 
dry  cell  to  the  electromagnet  terminals  and  rotate  the  armature 
as  before.  What  deflection  do  you  now  observe?  Repeat  the 
experiment  by  connecting  two  cells  in  series  with  the  electro- 
magnet. Does  the  deflection  vary  with  the  strength  of  the 
magnetic  field?  If  so,  how? 

170.  Theory. — This    experiment    illustrates    another    funda- 
mental principle  of  the  generator.     The  results  show  that  as 
the  bar  magnets  are  moved  out  the  induced  voltage  decreases. 
This  is  due  to  the  decrease  in  the  strength  of  the  magnetic  field. 
When  the  electromagnet  was  used  in  place  of  the  permanent  mag- 
nets the  deflection  was  greater.     This  was  due  to  the  fact  that 
the  electromagnet  provides  a  stronger  magnetic  field. 

As  the  armature  is  so  constructed  that  the  number  of  turns  can- 
not be  changed  readily  the  relation  between  the  number  of  turns 
on  the  armature  and  the  induced  voltage  cannot  be  shown  by 
means  of  a  simple  experiment.  This  relation  has,  however,  been 
explained  in  Chapter  III  where  it  was  shown  that  the  induced 
pressure  is  proportional  to  the  number  of  turns  in  series  on  the 
armature.  These  principles  have  been  expressed  in  algebraic 
form  as  follows: 

w_    n  * 
~*X108 

where  n  is  the  number  of  turns,  3>  is  the  total  magnetic  flux,  t  is 
the  time,  in  seconds,  of  cutting,  and  108  (  =  100,000,000)  is  a 
factor  necessary  for  converting  the  value  of  induced  pressure 
into  volts. 

171.  Kinds  of  Generators. — Electric  generators  are  classified 
in  accordance  with  the  manner  of  excitation;  that  is,  the  classifi- 
cation is  determined  by  the  manner  in.  which  the  magnetic  field 
is  produced.     There  are  thus  magneto,  series,  shunt,  compound 
and  separately  excited  generators. 

The  magneto  generator  was  illustrated  when  the  field  was  pro- 


INDUCED  CURRENTS 


179 


FIG.  110. 


duced  by  the  permanent  magnets.  Such  generators  are  never 
built  in  very  large  sizes,  although  they  are  extensively  used  for 
ringing  telephone  bells,  and  for  supplying  current  for  gas  and 
gasoline  engine  ignition. 

172.  Series  Generator. — The  principles  of  the  series  generator 
were  not  illustrated.     In  a  series  wound  generator  the  electro- 
motive force  of  the  generator  supplies  the 

current  for  excitation.  The  current  devel- 
oped in  the  armature  flows  through  the  wind- 
ings of  the  field  as  shown  in  Fig.  110. 

173.  Shunt  Generator. — In  a  shunt  gen- 
erator, the  field  is  excited  by  a  winding  that 
is  connected  in  parallel  with  the  outside  cir- 
cuit.     The    exciting    current    can   circulate 
through  the  field  winding  no  matter  whether 
the  external  circuit   is  closed  or    open.     A 
diagrammatic  sketch  of  such  a  generator  is  shown  in  Fig.  111. 
The  student  will  observe  that  one  end  of  the  field  winding  is 
connected  to  one  brush  at  a  and  after  passing  around  the  field 
poles  and  the  regulating  rheostat  it  is  connected  to  brush  6. 
The  current  developed  in  the  armature  divides  at  the  brushes; 
part  of  it  passes  through  the  field  winding  while  the  other  part 

passes  through  the  external 
circuit.  By  means  of  the 
rheostat  the  current 
through  the  field  winding 
is  regulated. 

174.  Compound  Genera- 
tor.— Both  the  series  and 
shunt  generators  have  cer- 
tain  disadvantages   which 
are  eliminated  by  a  com- 
bination of  the  two  wind- 
ings.    Such  a  machine  is  called  a  compound  generator.     The 
manner  in  which  the  winding  is  arranged  is  shown  in  Fig.  112. 

The  principles  of  separate  excitation  were  illustrated  by  the 
experiment  in  which  the  electromagnet  was  used.  In  this  ex- 
periment the  excitation  was  supplied  by  the  dry  cells.  In  prac- 
tice dry  cells  are  not  used,  but  usually  a  small  shunt  or  com- 
pound generator  is  employed.  This  is  the  method  used  in  nearly 
every  alternating-current  generator. 


FIG.  111. 


180 


MAGNETISM  AND  ELECTRICITY 


INDUCED  CURRENTS  181 

175.  The  Electric  Motor. — A  direct-current  generator  may  be 
used  as  a  motor  with  but  slight  modification.     The  difference 
between  a  direct-current  generator  and  a  direct-current  motor 
is  not  in  their  mechanical  construction,  but  in  their  manner  of 
operation.     A  generator  is  driven  by  mechanical  means,  and  in 
its  operation  converts  mechanical  energy  into  electrical  energy. 
The  motor  is  driven  by  electrical  means  and  converts  electrical 
energy  into  mechanical  energy.     We  have  learned  some  of  the 
principles  of  generating  an  elec- 
tromotive force  and  some  of  the 

characteristics  of  a  dynamo  when 
operated  as  a  generator.  We 
will  now  study  how  an  electric 
current  can  cause  a  dynamo  to 
operate  as  a  motor,  and  some  of 
the  characteristics  of  the  ma- 
chine when  so  operated.  In  or- 
der to  get  a  clear  understanding  .pIG>  112. 
of  the  fundamental  principles 
several  experiments  will  have  to  be  performed. 

176.  Experiment  39.    To  Investigate  the  Cause  of  Rotation 
of  Motor  Armature. 

Apparatus. — 

Motor  on  board 

Two  dry  cells 

Operation. — First  carefully  examine  the  winding  on  the  arma- 
ture and  note  carefully  the  direction  taken  by  a  current  if  the 
positive  terminal  of  a  dry  cell  is  connected  to  binding  post  A, 
Fig.  113.  Place  the  armature  in  the  position  indicated  in  the 
figure,  and  determine  the  polarity  of  the  ends  of  the  armature, 
assuming  that  the  current  flows  in  at  A  and  out  at  B.  If  you 
cannot  do  this  by  means  of  the  right-hand  rule,  swing  the  bar 
magnets  apart  and  remove  one  magnet  from  its  holder.  Connect 
the  carbon  electrode  of  one  dry  cell  to  binding  post  A  and  the 
other  or  cup  to  binding  post  B.  With  the  armature  in  such  a 
position  that  each  brush  touches  only  one  commutator  segment 
determine  the  polarity  of  the  armature  by  testing  with  the  bar 
magnet.  This  can  be  done  without  touching  the  magnet  to  the 
armature  core.  If  the  pole  of  the  armature  is  opposite  to  that 
of  the  end  of  the  bar  magnet  a  strong  attraction  will  result. 
Is  the  polarity  as  expected?  Replace  the  bar  magnet  within 


182 


MAGNETISM  AND  ELECTRICITY 


o 


its  holder  and  after  disconnecting  the  battery  swing  the  magnets 
into  place.  Assuming  that  the  current  enters  at  the  binding 
post  A,  and  remembering  that  unlike  poles  attract,  will  the  end 
of  the  armature  marked  C  be  attracted  by  the  TV-pole  or  by  the 
/S-pole  of  the  bar  magnet?  That  is,  in  which  direction  will  the 
armature  turn,  clockwise  or  counter-clockwise?  Now  connect 
the  cell  as  before  and  verify  your  conclusions.  Hold  the  arma- 
ture so  that  it  comes  to  rest  with  its  long  axis  parallel  to  the 

magnetic  field.  Note  the 
position  of  the  brushes. 
Turn  the  armature  by  hand 
in  the  direction  of  rotation 
until  the  brush  contacts 
change  segments.  What 
happens?  Why  does  the 
armature  move?  Has  the 
polarity  of  the  armature 
changed?  How  can  you 
account  for  this?  Why 
does  it  not  stop  after  mak- 
ing a  complete  one-half 
revolution? 

177.  Theory. — A  careful 
performance  of  the  forego- 
ing experiment  and  a 
thorough  study  of  the  prin- 
ciples will  give  the  student 
a  clear  understanding  of 
the  cause  of  rotation  of  the 
armatures  of  all  motors. 
In  many  cases  these  prin- 
ciples are  combined  with  others  and  thus  the  whole  process  is 
much  more  complicated  but  the  elements  are  the  same  in  every 
case.  The  cause  of  rotation  can  be  briefly  stated  to  be  due  to 
the  interaction  of  two  magnetic  fields.  One  field  is  due  to  the 
permanent  magnets  which  remain  fixed  in  position.  The  other 
is  due  to  the  current  flowing  through  the  armature  winding. 
This  field  reverses  its  direction  every  time  the  commutator  seg- 
ments change  brush  contacts. 

In  the  first  part  of  the  experiment  the  student  learned  that  the 
end  C  of  the  armature  core  is  a  >S-pole  while  D  is  a  AT-pole.     The 


FIG.  113. 


INDUCED  CURRENTS  183 

ends  of  the  bar  magnets  are  of  opposite  polarity  with  respect  to 
the  polarity  of  the  armature  core.  These  two  poles  are  attracted 
to  each  other,  causing  the  armature  to  move  counter-clockwise. 
When  the  armature  has  moved  a  little  beyond  the  middle  point, 
the  brushes  change  connection  with  the  commutator  segments 
thus  changing  the  direction  of  the  current  through  the  armature 
and  as  a  consequence  the  polarity  of  the  armature  core  is  also 
changed.  The  end  that  was  a  N-pole  becomes  a  $-pole,  and  vice 
versa.  Thus  the  end  C  of  the  armature  core  instead  of  being 
attracted  by  the  adjacent  pole  of  the  bar  magnet  is  repelled. 
The  same  conditions  prevail  at  the  end  D  of  the  armature.  When 
the  armature  has  made  one-half  of  a  rotation  the  brushes  again 
change  commutator  segments  and  thus  the  armature  continues 
to  rotate. 

178.  Experiment  40.    To  Determine  the  Direction  of  Rota- 
tion. 

Apparatus. — Same  as  in  preceding  experiment. 

Operation. — Exchange  the  battery  connections  and  with  the 
magnets  in  position  observe  the  direction  of  rotation  of  the  arma- 
ture. Has  it  reversed?  Can  you  explain  why?  Loosen  the 
nuts  that  hold  the  bar  magnets  in  place  and  change  them  end 
for  end,  and  again  determine  the  direction  of  rotation.  What 
conditions  determine  the  direction  of  rotation?  Turn  the  brush 
holder  around  as  far  as  it  will  go  and  see  if  the  armature  will 
rotate.  Why? 

One  method  of  varying  the  speed  is  by  shifting  the  brushes. 
With  two  cells  connected  in  series  and  the  motor  running  freely, 
turn  the  brush  holder  slowly  first  in  one  direction  and  then  in  the 
other  and  observe  the  effect  on  the  speed.  Explain  this. 

179.  Experiment  41.    To  Study  the  Relation  between  the 
Strength  of  the  Magnetic  Field  and  the  Speed  of  Rotation. 

Apparatus. — Same  as  in  Experiment  39. 

Operation. — Connect  one  cell,  ammeter,  and  motor  in  series 
and  while  the  armature  is  in  rotation  spread  the  bar  magnets 
and  observe  whether  the  speed  decreases  or  increases.  Does 
the  strength  of  the  magnetic  field  affect  the  speed?  How? 
Read  the  armature  current.  Replace  the  magnets  and  connect 
two  cells,  the  ammeter,  and  motor  in  series  and  compare  the 
resulting  speed  with  the  speed  when  only  one  cell  was  connected 
to  the  motor.  Also  read  the  resulting  current.  Does  the  speed 
vary  with  the  current  through  the  armature?  How? 


184  MAGNETISM  AND  ELECTRICITY 

180.  Theory. — The  student  will  have  to  be  careful  in  making 
general  conclusions  from  the  results  of  experiments  40  and  41. 
While  the  results  of  experiment  41  show  that  the  speed  decreases 
as  the  bar  magnets  are  moved  out  it  would  seem  that  a  decrease 
in  the  field  strength  decreases  the  speed.     This,   however,  is 
true  only   under   certain  conditions.     It  would  lead  to  great 
error  to  assume  that  such  is  the  case  in  practice.     The  reason 
for  this  seemingly  false  conclusion  will  be  stated  now,  and  the 
principles  will  be  illustrated  by  an  experiment  later.     In  the 
present  experiment  the  friction  of  the  brushes,  bearings,  and  air 
is  so  great  in  comparison  with  the  torque,  that  when  the  bar 
magnets  are  moved  out  the  field  is  weakened  and  consequently 
the  torque  and  speed  is  decreased.     By  torque  is  here  meant 
the  turning  effort  or  moment  which  is  produced  by  the  interac- 
tion of  the  magnetic  fields  due  to  the  current  in  the  armature 
windings  and  bar  magnets.     This  torque  is  proportional  to  the 
product  of  these  two  fields. 

The  field  due  to  the  armature  current  is  proportional  to  the  cur- 
rent and  in  this  experiment  this  current  is  almost  entirely  deter- 
mined by  the  resistance  of  the  circuit  which  consists  of  the  cell, 
connecting  wires,  brushes,  commutator,  and  armature  windings. 
If  this  were  not  so,  a  different  result  would  be  observed.  In  the 
second  part  of  the  experiment,  another  cell  was  added  and  ac- 
cordingly the  armature  current  was  increased.  This  increase  in 
armature  current  strengthens  the  armature  field  and  the  result- 
ing torque.  As  the  torque  is  increased  the  speed  is  increased. 

It  has  already  been  pointed  out  that  if  we  were  restricted  to 
the  use  of  permanent  magnets,  dynamos  of  large  capacity  would 
be  unknown.  The  next  experiment,  then,  will  be  to  determine 
the  effect  of  using  an  electromagnet  for  the  field  and  to  study 
some  characteristics  of  practical  motors. 

181.  Experiment   42.    To    Study    the    Characteristics    of    a 
Separately  Excited  Motor. 

Apparatus. — 
Motor  and  electromagnet 
Dry  cells 
Volt-ammeter 

Operation. — Connect  the  volt-ammeter,  one  dry  cell,  and  elec- 
tromagnet in  series  as  indicated  in  Fig.  114  and  then  connect 
one  cell  to  the  armature  binding  posts.  By  holding  your  finger 
against  the  armature  shaft  test  the  torque.  Is  the  torque  greater 


INDUCED  CURRENTS 


185 


or  less  than  when  permanent  magnets  were  used?  Why? 
With  one  of  the  bar  magnets  test  the  polarity  of  the  electromag- 
net. Is  the  electromagnet  any  stronger  than  the  bar  magnets? 
If  so,  do  you  think  this  has  anything  to  do  with  the  torque? 

Next,  connect  two  dry  cells  in  series  with  the  field  and  again 
observe  the  speed.  Has  the  speed  increased  or  decreased? 
Can  you  account  for  the  change?  In  each  case  read  and  record 
the  field  current.  After  measuring  the  current  through  the 
field,  remove  the  volt-ammeter  and  connect  it  into  the  armature 


FIG.  114. 

circuit;  close  the  armature  circuit  and  read  the  current  when  the 
armature  is  stationary.  Then  close  the  field  circuit  and  start 
the  armature.  Observe  the  behavior  of  the  ammeter  pointer 
while  the  motor  is  speeding  up.  Does  the  current  increase  or 
decrease?  Explain.  Repeat  this  until  you  are  certain  that 
you  have  made  no  mistake  in  reading  the  ammeter. 

182.  Theory. — The  general  principles  of  the  operation  of  the 
motor  are  the  same  in  this  as  in  the  preceding  experiments. 
The  only  difference  is  in  the  field  strength.  That  is,  the  electro- 


186 


MAGNETISM  AND  ELECTRICITY 


magnet  field  is  much  stronger  than  the  permanent  magnet  field. 
The  magnetic  field,  however,  is  not  as  strong  as  it  ought  to  be  on 
account  of  the  large  air  gap.  Commercial  motors  are  constructed 
so  that  the  magnetic  field  has  only  a  small  air  gap  to  cross,  and 
this  air  gap  remains  fixed  in  depth.  The  iron  cores  for  the  mag- 
netic field  of  Type  S,  Northern  motor,  is  shown  in  Fig.  115,  and 
a  diagram  showing  the  path  of  magnetic  lines  is  shown  in  Fig. 
116.  The  most  puzzling  result  is  undoubtedly  the  last  part  of 
the  experiment  where  it  is  shown  that  the  armature  current  de- 
creases as  the  speed  increases.  This  is  due  to  two  causes.  One 


FIG.  115. 

is  the  increase  in  the  resistance  of  the  brush  contacts,  for  as  the 
speed  increases  the  brushes  are  jarred  as  they  pass  over  the  slots. 
This  jarring  increases  the  resistance  and  decreases  the  current. 
The  decrease  in  current  is  not  wholly  due  to  the  increase  in 
resistance,  as  a  little  reasoning  will  show. 

In  experimenting  with  the  dynamo  as  a  generator  it  was  shown 
that  as  the  armature  rotated  within  the  magnetic  field,  an  elec- 
tromotive force  was  developed  which  caused  a  deflection  of  the 
ammeter.  The  same  conditions  for  generating  an  electromotive 
force  are  present  in  this  experiment  as  in  experiment  36.  We 


INDUCED  CURRENTS  187 

have  a  magnetic  field  within  which  the  armature  is  rotated.  If 
the  rotation  of  the  armature  within  a  magnetic  field  develops 
an  electromotive  force  in  one  case,  it  will  in  every  case  when  the 
same  conditions  are  present.  In  the  generator  experiment,  how- 
ever, it  was  possible  to  detect  the  generated  e.m.f.  This  is  not 
so  easily  done  in  this  case,  hence  its  presence  must  be  determined 
in  some  other  way.  As  the  armature  speeds  up  the  winding 
cuts  the  field  at  an  increased  rate.  As  has  been  shown,  whenever 
an  electromotive  force  is  developed  by  the  motion  of  a  conductor, 
the  induced  pressure  is  always  in  such  a  direction  as  to  oppose 
the  motion.  Accordingly,  the  induced  pressure  must  be  in  such 
a  direction  as  to  oppose  the  applied  pressure  or,  as  it  is  called,  it 
must  be  a  counter  pressure.  That  this  must  be  so  can  be  seen 
readily  by  considering  what  would  happen  if  the  induced  pressure 
were  in  the  same  direction  as  the  applied  pressure.  As  the  motor 


FIG.  116. 

speeded  up  the  induced  pressure  would  be  added  to  the  applied 
pressure  and  according  to  Ohm's  law  a  larger  current  would 
flow  through  the  armature.  This  increase  in  current  would 
increase  the  torque,  which  in  turn  would  raise  the  speed.  Any 
increase  in  speed  would  of  course  increase  the  induced  pressure 
and  so  the  process  would  go  on  indefinitely  until  the  motor  was 
destroyed.  In  other  words,  the  motor  would  have  to  be  loaded 
to  prevent  its  running  away  or  we  may  say  " perpetual  motion" 
would  result.  The  induced  pressure  opposes  the  applied  pressure 
and  as  the  speed  increases,  the  counter  pressure  increases  reducing 
the  current.  This  current  is  reduced  to  such  a  point  that  the 
torque  is  just  great  enough  to  overcome  the  friction  at  a  definite 
speed.  If  the  speed  is  decreased  below  this  point,  the  counter 
pressure  is  decreased,  more  current  flows  through  the  armature 
and  a  greater  torque  results.  An  increase  in  speed  increases  the 
19 


188  MAGNETISM  AND  ELECTRICITY 

counter  pressure  and  less  current  is  taken  by  the  armature,  and 
the  torque  is  correspondingly  reduced.  The  speed  then  is  de- 
termined by  the  field  strength,  the  applied  pressure  and  friction, 
and  so  long  as  these  quantities  are  constant  the  speed  of  the 
separately  excited  motor  is  constant.  A  practical  motor  running 
idle  will  behave  the  same  way. 

In  this  small  motor  the  armature  current  is  determined  more 
by  the  resistance  of  the  circuit  than  by  the  counter  pressure  and 
for  this  reason  it  does  not  behave  exactly  as  a  larger  machine, 
but  has  some  of  the  characteristics  of  a  direct-current  watthour 
meter,  whose  voltage  coil  current  is  determined  by  the  resistance 
of  the  armature.  If  the  armature  had  many  more  turns,  and  the 
field  could  be  made  much  stronger,  the  relation  of  the  speed  to 
the  field  strength  would  be  materially  changed.  When  a 
commercial  motor  is  operated  a  weakening  of  the  field  reduces 
the  counter  pressure,  and  more  current  flows  through  the  arma- 
ture. This  increase  in  current  increases  the  torque  and  the 
armature  speeds  up  until  the  counter  pressure  is  increased  suf- 
ficiently to  again  control  the  current  flow,  and  the  torque  is 
just  sufficient  to  carry  the  load  or  keep  the  motor  running  at 
that  speed.  A  further  decrease  in  the  field  strength  will  be 
followed  by  a  further  increase  in  speed  and  a  strengthening  of 
the  field  will  cause  a  decrease  in  the  speed.  Thus  by  strengthen- 
ing and  weakening  the  field  a  wide  range  of  speed  is  obtained. 
This  method  of  controlling  the  speed  is  quite  common  in  practice. 
Although  these  principles  cannot  be  fully  illustrated  with  the 
small  motor,  that  the  conclusions  are  true  can  be  shown  by  the 
following  experiment. 

183.  Experiment  43.  To  Study  the  Operation  of  Series 
Motor 

Apparatus. — Same  as  in  preceding  experiment. 

Operation. — Connect  three  dry  cells,  motor,  and  ammeter  in 
series  as  shown  in  Fig.  117.  To  make  a  series  connection  on 
the  motor,  connect  one  end  of  electromagnet  coil  to  a  terminal 
of  a  dry  cell,  and  the  other  end  of  the  electromagnet  coil  to  one 
binding  post  on  the  brush  holder.  Connect  the  other  binding 
post  of  the  motor  to  one  terminal  of  the  ammeter,  and  connect 
the  other  ammeter  terminal  through  a  switch  to  the  other  free 
binding  post  on  the  cells.  When  such  a  connection  is  made  the 
current  must  pass  through  the  armature  and  field  coils  in  series, 
and  accordingly  a  motor  so  connected  is  called  a  series  motor. 


INDUCED  CURRENTS 


189 


Close  the  switch  and  measure  the  current  with  the  armature 
stationary.  Record  this  value.  Then  start  the  armature  while 
the  push-button  on  the  ammeter  is  kept  closed.  Does  the  current 
increase  or  decrease  as  the  speed  of  the  armature  increases? 

184.  Theory. — In  the  series  motor  the  current  flows  in  series 
through  the  armature  and  the  field.  As  the  speed  increases 
the  counter  pressure  increases,  which  decreases  the  current  with 
a  resultant  weakening  of  the  field.  The  experiment  thus  shows 
that  a  decrease  in  the  field  strength  is  accompanied  by  an  in- 


FIG.  117. 

crease  in  the  speed.  Furthermore,  in  the  series  motor  these 
two  things  go  on  together  so  that  the  speed  is  controlled  only 
by  the  friction  and  the  load.  An  unloaded  series  motor  has  the 
tendency  to  speed  up  and  if  permitted  the  speed  may  reach  a 
high  enough  value  to  destroy  the  armature.  This  of  course  will 
not  take  place  with  the  small  experimental  motor  when  only 
three  dry  cells  are  used.  On  account  of  the  speed  characteristics 
of  the  series  motor  it  should  always  be  direct  connected  to  the 
load. 


190  MAGNETISM  AND  ELECTRICITY 

185.  Experiment  44.     To  Study  the  Shunt  Motor. 

Apparatus. — Same  as  in  the  preceding  experiment. 
Operation. — Connect  the  terminals  of  the  electromagnet  under 
the  lower  nuts  on  the  brush  holder  binding  posts.  Connect  two 
dry  cells  in  series  and  then  connect  the  two  free  terminals  to 
the  same  binding  posts,  and  observe  the  operation  of  the  motor. 
A  motor  connected  in  this  way  is  called  a  shunt  motor.  Observe 
the  direction  of  rotation  and  then  exchange  the  battery  con- 
nections. Has  the  direction  of  rotation  changed?  Why? 
Leave  the  battery  connections  as  before  and  exchange  the  field 
connections.  Have  you  reversed  the  direction  of  rotation? 
Explain.  Again  change  the  battery  connections  and  note  the 
direction  of  rotation.  In  what  way  can  you  change  the  direction 
of  rotation  of  a  shunt  motor?  The  working  out  of  the  answers 
to  the  foregoing  questions  will  be  left  to  the  student. 

186.  The    Compound    Motor. — In   a    compound   motor    the 
field  winding  consists  of  two  parts.     One  part  is  connected  in 
series  with  the  armature  and  the  other  in  shunt  as  in  the  pre- 
ceding experiment.     When  the  two  windings  are  connected  so 
that  the  two  fields  reinforce  each  other  the  winding  is  called 
cumulative  compound.     When  the  series  field  opposes  the  shunt 
field  the  winding  is  called  differential  compound. 

RECAPITULATION 

1 .  The  electric  generator  is  a  machine  for  the  transformation  of  mechanical 
into  electrical  energy. 

2.  The  electromotive  force  of  a  generator  is  developed  by  rotating  the 
conductors  wound  on  an  iron  core  across  a  magnetic  field. 

3.  Electric  generators  are  classified  in  accordance  with  the  method  of 
excitation.     There  are  thus  magneto,  shunt,  series,  and  compound 
generators. 

4.  A  magneto  is  an  electric  generator  whose  excitation  is  supplied  by 
permanent  magnets. 

5.  A  shunt  generator  is  one  whose  field  is  excited  by  a  current  flowing 
through  the  field  coils  which  are  connected  in  parallel  with  the  ex- 
ternal circuit. 

6.  A  series  geenrator  is  one  whose  field  is  excited  by  a  current  flowing 
from  the  armature  through  field  coils  which  are  connected  in  series 
with  the  external  field. 

7.  A  compound  wound  generator  is  one  which  contains  both  a  shunt 
and  series  winding. 

8.  With  reference  to  excitation  direct-current  motors  are  classified  in 


INDUCED  CURRENTS 


191 


192  MAGNETISM  AND  ELECTRICITY 

the  same  manner  as  generators.     That  is,  there  are  series,  shunt,  and 
compound  motors. 

9.  Compound-wound  direct-current  motors   are  of  two  classes,  cumu- 
lative compound,  and  differential  compound. 

(a)  A  cumulative  compound  motor  is  one  in  which  the  compound 
winding  reinforces  the  shunt  winding. 

(b)  A  differential  compound  motor  is  one  in  which  the  compound 
winding  opposes  the  shunt  winding. 


CHAPTER  X 
WORK  AND  ENERGY 

187.  Work. — The  industrial  application  of  electricity  is  mainly 
a  process  of  utilizing  energy.     That  is,  all  industrial  work  from  a 
physical  viewpoint  is  nothing  but  a  conversion  of  energy.     Every- 
one has  some  idea  of  the  meaning  of  the  word  work.     Every 
farmer  knows  that  even  where  the  roads  are  alike  in  every  respect, 
twice  as  much  work  is  done  in  hauling  a  given  load  two  .miles 
as  in  hauling  the  same  load  one  mile.     The  pull  or  force  exerted 
by  the  horses  is  the  same  in  the  two  cases,  but  the  distance  is 
twice  as  great  in  the  first  as  in  the  second  case.     In  hoisting  a 
load  of  2  tons  to  the  top  of  a  building  twice  as  much  work  is  done 
as  when  only  1  ton  is  moved  through  the  same  distance.     In  this 
illustration  the  distances  are  the  same,  but  the  loads  or  weights 
lifted  are  different.     In  general,  there  are  two  factors  that  enter 
into  work — force  and  distance.     The  physical  definition  of  work 
takes  these  into  consideration.     Thus,  work  is  the  result  of 
moving  a  body  against  a  force  and  is  measured  by  the  product 
of  the  force  into  the  distance,  in  the  direction  of  the  force. 
Algebraically  this  is  expressed  by 

work,  W=FXd 

In  the  above  definition,  the  phrase  "in  the  direction  of  the  force" 
must  be  noted  carefully.  For  instance,  moving  a  load  of  100  Ib. 
vertically  through  a  distance  of  100  ft.  will  require  more  work 
than  to  move  the  same  load,  or  weight,  the  same  distance  along 
a  smooth  horizontal  plane. 

188.  Unit  of  Work. — In  the  English  system  of  units,  the  unit 
of  work  is  the  foot-pound  and  is  represented  by  the  quantity  of 
work  done  in  raising  a  pound  weight  1  ft.  against  the  force  of 
gravity.     In  the  metric  system,  the  unit  of  work  is  called  the 
erg  and  is  the  quantity  of  work  done  by  a  force  of  one  dyne  acting 
through  a  distance  of  1  cm.     The  erg  is  a  very  small  quantity 
and  hence  10,000,000  (  =  107)    ergs  are  taken  as  the  practical 
unit.     The  practical  unit  is  called  the  joule. 

21  193 


194  MAGNETISM  AND  ELECTRICITY 

EXAMPLES 

1.  How  many  foot-pounds  of  work  are  done  by  a  hod  carrier  in  carrying  a 
load  of  bricks  weighing  40  Ib.  up  a  ladder  20  ft.  high? 

Solution. — 

W=FXd 
F  =401b. 
d   =20  ft. 
And  TF  =  40X20  =  800  ft.-lb. 

2.  The  lifting  magnet  shown  in  Fig.  44  hoisted  at  one  load  a  ton  of  pig  iron 
to  an  elevation  of  25  ft.     How  much  work  did  it  do? 

Solution. — 

W=FXd 
F  =  2,000  Ib. 
d   =25  ft. 
Hence          W  =  2,000  X  25  =  50,000  f t-lb.' 

3.  How  many  ergs  in  1  ft.-lb.  ? 

Solution. — 

1  Ib.      =445,000  dynes 
1  ft.      =30.48  cm. 
1  ft.-lb.  =  1  ft.  XI  Ib. 

=  445,000X30.48 
=  13,563,600  ergs 

4.  How  many  joules  in  1  ft.-lb.? 

Solution. — 

1  joule  =  107  ergs 
1  ft.-lb.  =  13,563,600  ergs. 
Hence  1  ft.-lb.  =  13,563,600  4- 107 

=  1.356  joules 

189.  Energy. — Energy  and  work  are  closely  related.  When  a 
weight  has  been  lifted  to  a  certain  height,  a  definite  amount  of 
work  has  been  done  upon  it.  This  work  in  foot-pounds  is  equal 
to  the  product  of  the  height  in  feet  by  weight  in  pounds.  The 
weight  at  the  top  possesses  something  which  it  does  not  possess 
at  the  bottom.  Similarly,  water  at  the  top  of  Niagara  Falls 
is  capable  of  doing  work  by  being  run  through  a  water  wheel. 
When  it  leaves  the  water  wheel  and  enters  the  river  at  the  bottom 
of  the  falls,  it  is  no  longer  capable  of  doing  work.  That  is,  it 
has  parted  with  its  ability  to  do  work  in  descending  from  the  top 
to  the  bottom  of  the  falls.  The  energy  of  a  body  or  a  system 
of  bodies  is  its'  capacity  for  doing  work.  It  is  measured  by  the 
work  which  can  be  performed.  Energy  is  classified  under  two 


WORK  AND  ENERGY  195 

heads  potential  and  kinetic.  The  energy  that  a  body  possesses 
by  virtue  of  its  position  is  called  potential.  Thus,  the  water  at 
the  top  of  the  falls  is  capable  of  doing  work  on  descending  to  a 
lower  level.  It  thus  possesses  energy  of  position.  Similarly,  a 
weight  lifted  to  a  given  height  possesses  energy  of  position. 
If  the  weight  be  dropped,  the  elevation  will  decrease,  but  its 
energy  will  not  decrease  until  it  strikes  the  earth  and  transfers 
its  energy  to  some  other  body.  When  only  a  short  distance, 
say  1  ft.,  from  the  lowest  point  in  its  fall,  its  energy  of  position 
is  very  small,  and  just  before  it  strikes,  the  energy  of  position 
is  practically  zero.  The  velocity  of  the  body  is  maximum  or 
greatest  at  the  time  of  striking,  and  zero  at  its  highest  point. 
The  body  possesses  energy  by  virtue  of  its  velocity.  This  energy 
due  to  the  velocity  of  the  body  is  called  kinetic.  The  simple 
pendulum  will  help  make  this  clear.  The  simple  pendulum  at 
the.extreme  position  of  its  swing  possesses  energy  due  to  its  eleva- 
tion. When  released,  this  elevation  decreases  until  the  pendulum 
reaches  the  lowest  point  of  its  swing  when  its  elevation  is  zero, 
but  its  velocity  is  a  maximum.  The  potential  energy  has  all  been 
changed  to  kinetic.  As  the  pendulum  passes  beyond  the  middle 
point  of  its  swing,  the  velocity  decreases,  hence  the  kinetic  energy 
decreases.  The  elevation  of  the  pendulum  increases,  and,  there- 
fore, the  potential  energy  increases.  This  change  continues  until 
the  pendulum  reaches  the  other  extremity  of  its  swing,  when  the 
energy  is  again  wholly  potential.  The  sum  total  of  the  energy  of 
the  pendulum  is  constant  at  any  point  of  the  swing.  That  is, 
the  sum  of  its  kinetic  and  potential  energy  is  a  constant  quantity. 
As  already  stated,  the  unit  of  energy  is  the  same  as  the  unit 
of  work,  and  the  energy  of  a  body  is  equal  to  the  amount  of  work 
expended  upon  the  body.  This  is  a  simple  statement  of  the 
fundamental  principles  of  dynamics,  viz.,  the  Principle  of  the 
Conservation  of  Energy.  Newton  limited  his  laws  to  motion, 
in  reality  they  may  be  considered  as  applying  to  energy  as  well. 
Thus,  the  statement  "action  is  equal  to  reaction"  is  also  true 
with  reference  to  the  expenditure  of  energy.  No  body  is  capable 
of  doing  work  unless  work  is  first  done  upon  it.  All  machines 
act  simply  as  means  of  transferring  energy  from  one  system  to 
another  system.  The  full  appreciation  of  this  principle  is  of 
comparatively  recent  date.  Perhaps  the  most  important 
discovery  in  the  realm  of  mechanics  is  the  following:  The  sum  of 
the  kinetic  and  potential  energies  of  a  body  or  system  of  bodies 


196  MAGNETISM  AND  ELECTRICITY 

is  a  constant  quantity,  unless  it  be  changed  by  some  external 
influence.  In  other  words,  the  energy  of  a  system  cannot  be 
created  or  annihilated.  No  human  being  can  create  or  destroy 
energy.  A  distinction  must,  however,  be  made  between  the 
total  amount  of  energy  of  a  body  or  system  of  bodies,  and  the 
amount  of  energy  that  the  system  is  capable  of  transferring  to 
another  system.  In  all  mechanical  operations  some  energy  is 
dissipated  or  wasted  or  becomes  unavailable.  For  instance,  a 
simple  pendulum  released  at  the  extreme  position  of  its  swing, 
will  not  of  itself  reach  the  same  point  on  its  return.  This  is 
due  to  the  fact  that  some  of  its  energy  has  been  transferred  to 
the  air,  and  another  portion  has  been  dissipated  on  account  of 
the  friction  and  stiffness  of  the  string  supporting  it.  This  law 
of  the  conservation  of  energy  is  fundamental  in  all  energy 
transformations. 

190.  Power. — In  everyday  usage,  the  word  power  has  many 
different  meanings.     It  is  often  confused  with   work.     Power 
is  not  work,  but  the  time  rate  of  doing  work.     As  an  illustration 
suppose  that  one  man  carries  2,000  bricks  to  the  second  story  of 
a  building  in  one  day  while  it  takes  another  man  two  days  to  do 
the  same  work.     Evidently,  the  total  amount  of  work  done  in 
the  two  cases  is  the  same  although  the  rate  at  which  the  work  is 
done  is  different.     The  second  man's  rate  of  doing  the  work 
is  only  one-half  that  of  the  first  man's  rate.     Technically  this 
is  explained  by  saying  that  the  power  of  the  two  men  is  different. 
The  power  of  the  first  man  is  double  that  of  the  second  man. 
Power  is  then  the  amount  of  work  done  in  some  unit  of  time. 
In  engineering  practice  the  unit  of  time  is  usually  the  minute 
or  second.     In  algebraic  symbols  power  is  expressed  by 

Work     w 

Power>P=Time=7 
FXd 
t 

or  Pxt=FXd=  work 

191.  Units  of  Power. — In  the  English  system  of  units  the  unit 
of  power  is  the  rate  of  doing  33,000  ft.-lb.  of  work  in  one  minute. 
This  unit  is  called  the  horse-power.     In  the  metric  system  of 
units  which  is  used  in  electrical  work  the  unit  of  power  is  the  watt. 
The  watt  is  defined  as  the  rate  of  doing  one  joule  per  second. 


WORK  AND  ENERGY  197 

It  is  very  important  that  the  distinction  between  power  and  work 
be  clearly  understood. 

EXAMPLES 

1.  Niagara  falls  are  about  160  ft.  high.  It  is  estimated  that  700,000  tons 
of  water  pass  over  them  every  minute.  If  all  of  the  energy  of  this  water 
could  be  utilized,  what  horse-power  could  be  developed? 

Solution. — 

work 


Power  = 


time 


The  work  or  energy  of  the  700,000  tons  of  water  is  700,000X2,000X160 
ft.-lb.     1  h.p.  =33,000  ft.-lb.  per  minute. 

700000X2000X160 
Hence,  Power  = 


=  6,787,878  h.p. 

2.  How  many  watts  in  1  h.p.? 

In  the  solution  of  example  4,  page  194,  it  was  shown  that  1  ft.-lb  was  equal 
to  1.356  joules.  One  horse-power  is  equal  to  550  ft.-lb.  per  second;  hence 
1  h.p.  must  equal  550X1.356  =  746  joules  per  second.  Since  one  watt 
equals  one  joule  per  second,  then  1  h.p.  equals  746  watts. 

3.  How  many  kilowatts  of  power  could  be  developed  from  Niagara  falls  if 
all  of  the  energy  were  utilized. 

Solution.  —  Since  1  h.p.  equals  746  watts  the  total  watts  developed  would 
be 

6,787,878X746  watts 

But  one  kilowatt  =  1,000  watts, 
Hence  kilowatts  developed  is 

K         6787878X746 

1000 
=  4,953,657  kw. 

192.  Electricity  and  Electrical  Energy.  —  It  is  impossible  at 
present  to  explain  electricity  in  terms  of  anything  simpler. 
We  know  electricity  only  through  its  manifestations  or  effects. 
It  matters  not,  so  far  as  practical  results  are  concerned,  whether 
electricity  is  a  form  of  energy  or  only  a  vehicle  of  energy.  The 
fact  is  that  energy  is  always  manifest  in  connection  with  the  elec- 
trical current,  and  that  this  energy  can  be  transformed  into  other 
forms  of  energy.  It  may  also  be  transferred  from  point  to  point 
along  a  conductor  without  the  necessity  of  mass  motion.  It  is 
this  ability  to  transfer  energy  without  the  motion  of  masses  of 
matter  that  makes  electricity  the  most  successful  medium  for 


198  MAGNETISM  AND  ELECTRICITY 

transferring  energy  over  long  distances.  The  transformation  of 
electrical  energy  is  electrical  work  and  is  accomplished  in  many 
ways.  The  rate  of  transformation  is  power  just  as  in  the  case 
of  other  forms  of  energy. 

193.  Electrical  Work. — The  derivation  of  the  principles  of 
electrical  work  or  energy  will  undoubtedly  be  better  understood 
if  analogies  are  used.  The  quantity  of  water  flowing  through 
any  pipe  in  a  given  time  may  be  expressed  as  the  strength  of  cur- 
rent multiplied  by  the  time.  A  unit  current  of  water  has  no  name. 
If  a  unit  current  gives  a  cubic  foot  (62.3  Ib.)  of  water  in  one  second, 
a  two-unit  current  will  give  2  cu.  ft.  of  water  per  second  or  10  cu. 
ft.  in  5  seconds. 

Similarly,  a  unit  current  of  electricity  flowing  for  1  second 
gives  a  definite  quantity  of  electricity.  This  quantity  is  called 
the  coulomb.  The  total  quantity  conveyed  by  a  constant  current 
of  /  amperes  in  t  seconds  is  then  given  by  Q  =  It.  Again  referring 
to  the  analogy  of  water  flowing  through  pipes  one  may  consider 
unit  work  to  be  done  when  1  cu.  ft.  of  water  is  delivered 
under  a  head  of  1  ft.  The  amount  of  work  done  by  a  head  of 
h  feet,  delivering  q  cubic  feet  of  water  will  be  hq.  But  electrical 
pressure  is  analogous  to  water  pressure,  or  head,  and  the  quantity 
of  water  is  analogous  to  the  quantity  of  electricity  or  coulombs 
A  current  delivering  Q  coulombs  of  electricity  under  a  pressure 
of  E  volts  will  then  do  EQ  units  of  work.  This  may  be  expressed 
algebraically,  thus: 

work   =  E  (volts)  X  Q  (coulombs) 
=  EQ  joules 

The  values  of  volts,  coulombs,  and  joules  have  been  so  selected 
that  the  product  of  one  volt  by  one  coulomb  gives  one  joule. 
It  has  been  shown,  however,  that  Q,  the  quantity,  is  equal  to 
It,  the  current  by  the  time.  We  may  then  write  the  expression 
for  work  thus: 

Work,  w,=EIt. 

When  E  is  in  volts,  /  in  amperes  and  t  in  seconds  the  result  is  in 
joules.  If  t  is  1  second,  we  have 

w  =  EI  joules,  per  second. 

One  joule  per  second  is  1  watt,  hence  in  general,  volts  X 
amperes  gives  watts.  In  electrical  work  the  joule  is  a  small 


WORK  AND  ENERGY  199 

unit  of  energy  so  1,000  watts  for  1  hour  is  usually  used.     This 
unit  is  called  the  kilowatt-hour.     It  is  equal  to  3,600,000  joules- 

EXAMPLES 

1.  What  power  is  being  developed   by  a  direct-current  generator  when  it 
gives  out  75  amperes  under  a  pressure  of  220  volts? 

Solution.  — 
Power  in  watts  =  volts  X  amperes 

-IXE 

I  =  75  amperes 
#  =  220  volts 

Hence          P  =  75  X220  =  16,500  watts 
1,000  watts     =lkw. 
Then  P  =  16,500  -=-  1,000  =  16.5  kw. 

2.  A  house  is  lighted  with  100  lamps  each  taking  0.55  ampere  at  110  volts. 
How  many  watts  are  necessary  to  operate  the  lamps? 

Solution.  —  Since  each  lamp  takes  0.55  amperes,  and  incandescent  lamps 
are  usually  connected  in  parallel,  then  the  total  current  is  0.55X100  =  55 
amperes. 

Watts  =  55  XI  10 
Watts  =  6,050 

3.  The  armature  current  of  a  400-volt  direct-current  motor  is  30  amperes  at 
a  certain  load.     Neglecting  armature  losses,  how  much  electrical  power 
is  converted  into  work? 

Solution.  — 


=  30X400 

=  12,000  watts 

=  12  kw. 

4.  What  is  the  horse-power  developed  by  the  motor  in  example  3? 

Solution.  — 

1000  , 
1  kw.=  h.p. 


Hence  12  kw.  =  —7—  =  16.1  h.p. 

194.  Power  Drop.  —  According  to  Ohm's  law  the  pressure  drop 
across  a  resistance  R}  when  a  current  of  I  amperes  is  flowing, 
is  IXR  or 


200  MAGNETISM  AND  ELECTRICITY 

If  E  is  the  pressure  which  sends  a  current  of  I  amperes  through 
the  resistance,  then  the  power  spent  in  the  wire  is  IE  watts. 
Multiplying  both  sides  of  E  =  IR  by  I  we  get 

EI  =  PR 

Since  IE  is  the  power  spent  in  the  resistance,  and  IE  = 
PR,  then  the  power  loss  is  equal  to  PR  watts.  That  is,  the 
power  spent  in  forcing  a  current  through  a  resistance  is  equal 
to  the  square  of  the  current  multiplied  by  the  resistance. 

EXAMPLE 

1.  The  resistance  of  an  electric  flatiron  is  25  ohms.     What  is  the  power 
spent  in  the  iron  when  it  takes  4.5  amperes? 

Solution. — 

Power  =I*R 
I  =4.5 
R  =25 

Then     P      =4.5X4.5X25 
=  506.25  watts 

2.  If  the  electrical  energy  costs  12  cents  a  kilowatt-hour,  how  much  will  it 
cost  to  operate  the  iron  for  3  hours? 

Solution. — 

1  kw.-hr.  =  1,000  watts  for  1  hour 
506.25  watts  =  0.506  kw. 

0.506X3  =  1.518  kw.-hr.  used. 
1.518X0.12  =  18.2  cents,  cost  of  operating  the  flatiron  for  3  hours. 

3.  A  projection  lantern  is  operated  on  a  110-volt  circuit.     The  resistance 
of  the  controlling  rheostat  is  3.5  ohms.     If  the  voltage  drop  across  the 
lamp  is  50  volts  what  current  does  the  lamp  take  and  how  much  power  is 
wasted  in  the  rheostat? 

Solution. — The  voltage  drop  across  the  rheostat,  which  must  be  the  differ- 
ence between  the  drop  across  the  lamp  and  supply  voltage,  is  110—50  =  60 
volts.  By  Ohm's  law, 

I       -E 
~R 

E      =60 

R      =3.5 
AO 
Then  /       =«,_  =  17.1  amperes 

The  power  loss  is  I2R  =17.1X17.1X3.5 

=  1,028  watts,  nearly 

195.  Heating  Value  of  the  Electric  Current.— The  student 
has  observed  the  heating  effect  of  the  electrical  current  in  con- 


WORK  AND  ENERGY  201 

nection  with  several  of  the  experiments.  The  relation  between 
the  quantity  of  the  electrical  energy  and  the  quantity  of  heat 
has  not  been  explained.  The  power  loss  in  a  conductor  is  given 
by  I2R.  This  is  all  converted  into  heat  and  the  exact  relation 
was  first  determined  by  James  Prescott  Joule,  an  English  physi- 
cist. He  did  this  by  immersing  a  conductor  of  known  resistance 
into  a  known  weight  of  water  and  measuring  the  current,  time 
and  temperature.  The  results  of  his  experiments  show  that 
the  heat  generated  in  a  conductor  is  proportional  to  the  time,  to  the 
resistance,  and  to  the  square  of  the  current.  This  condition  may 
be  written  in  algebraic  form  as  follows: 


This  is  evidently  the  energy  loss  in  a  conductor  multiplied  by  a 
conversion  factor  K.  This  factor  is  introduced  on  account  of 
the  fact  that  the  unit  for  the  measurement  of  heat  is  not  the  same 
as  that  for  the  measurement  of  electrical  energy.  The  unit 
for  heat  measurement  is  the  quantity  of  heat  required  to  raise 
the  temperature  of  1  grm.  of  water  from  15  to  16  degrees 
cent.,  and  is  called  a  calorie.  The  calorie  is  equal  to  4.181  joules. 
That  is,  the  heat  unit  is  4.181  times  the  electrical  unit.  To  con- 

vert joules  to  calories  we  must  multiply  the  joules  by  T~yoy  = 

0.24.     This  0.24  is  the  constant  K  which  we  can  replace  and  get 

Heat,  in  calories,  =Q.24PRt 

where  I  is  in  amperes,  R  in  ohms,  and  t  in  seconds. 

The  mechanical  engineering  unit  of  heat  is  called  the  British 
thermal  unit,  which  is  abbreviated  to  B.t.u.  A  B.t.u.  is  the  heat 
required  to  change  the  temperature  of  1  Ib.  of  water  1  degree 
Fahrenheit.  One  B.t.u.  =252  calories. 

EXAMPLES 

1.  How  many  calories  of  heat  are  developed  in  a  flatiron  per  hour  if  the  iron 
takes  5  amperes  at  120  volts? 

Solution.  — 

Heat  =  0.24/2/ft 
7  =  5  amperes 
R  =  24  ohms 
t=  3,600  seconds 

Then  ff  =  0.24X5X5X24X3,600 

=  518,400  calories 


202 


MAGNETISM  AND  ELECTRICITY 


It  is  perhaps  a  little  simpler  if  we  remember  that  IzRt  =EIt.     For 
5X120X3,600  =  5X5X24X3,600 

It  is  not  necessary  to  find  the  resistance  first. 

2.  A  62-in.  Cutler-Hammer  lifting  magnet  takes  55  amperes  at  220  volts. 
This  is  all  converted  into  heat  after  the  magnetic  field  is  built  up.  How 
many  calories  of  heat  are  developed  in  the  winding  in  5  minutes? 


Solution. — 


Then 


Heat  =  0.24  Eli 
#  =  220  volts 
7  =  55  amperes 
t=  300  seconds 
H  =  0.24  X220X55  X300 
=  871,200  calories 


This  amount  of  heat,  will  raise  the  temperature  of  100  Ib.  of  iron  about 
170  degrees  cent,  in  the  same  time.  This  fact  shows  the  necessity  of 
designing  the  magnet  so  that  the  heat  produced  in  the  coil  may  be  con- 
ducted to  the  outside  quickly  and  easily  and  radiated  into  space. 

196.  Some  Practical  Applications  of  the  Heating  of  Electric 
Currents. — Undoubtedly  the  most  common  application  of  the 
heating  of  an  electric  current  is  the  incandescent  lamp.  The  con- 
ductor in  one  type  of  incandescent  lamp  consists  of  a  carbon  fila- 
ment enclosed  in  a  glass  globe  from  which  all  air  has  been 
exhausted.  The  light  is  produced  by  the  current  heating  the 


FIG.  118. 


FIG.  119. 


filament  to  a  bright  yellow.  A  16-candle-power  lamp  designed 
for  a  110-volt  circuit  has  a  resistance  of  about  200  ohms  when 
hot  and  takes  a  current  of  about  0.55  ampere.  It  is  called  a 
60-watt  lamp. 

Within  recent  years  metallic  filament  lamps  have  to  a  great 
extent  displaced  the  carbon  lamps.     The  best  lamps  of  this  type 


WORK  AND  ENERGY 


203 


have  a  filament  of  an  alloy  of  tungsten  and  osmium.  The  metal 
tungsten  has  a  high  melting-point  and  may  be  heated  to  a  higher 
temperature  than  carbon  before  it  disin- 
tegrates. This  property  makes  the  lamp 
more  efficient  by  converting  a  greater 
percentage  of  the  electrical  energy  into 
light.  The  present  tungsten  lamps  use 
about  1.25  watts  per  candle-power.  The 
General  Electric  Company  is  making 
preliminary  announcements  of  new  lamps 
whose  efficiency  is  much  better.  The 
lamp  will,  perhaps,  be  on  the  market  by 
the  time  this  text  is  off  the  press.  A  car- 
bon and  a  tungsten  lamp  are  shown  in 
Figs.  118  and  119. 

The  use  of  electrical  energy  for  the  pro- 
duction of  high  temperatures  has  resulted 
in  the  production  of  materials,  such  as 
carborundum,  tungsten,  commercial  gra- 
phite, emery,  calcium  carbide,  aluminum, 
etc.  The  electric  furnace  has  created  an 
entirely  new  industry;  before  the  application  of  high  tempera- 


FIG.  121. 


tures  was   possible,  the  above-named   materials   could  not   be 
produced  at  reasonable  cost  or  in  commercal  quantities. 


204  MAGNETISM  AND  ELECTRICITY 

Other  common  practical  applications  of  the  heating  effect  of 
electric  currents  are  the  many  forms  of  arc  lamps.  The  old 
style  of  carbon  arc  lamp  is  also  being  displaced  by  new  forms. 
One  form  called  the  flaming  arc  lamp  is  shown  in  Fig.  120. 

Wherever  electric  energy  is  comparatively  cheap  the  heating 
effect  of  the  electrical  current  may  be  used  to  operate  many  heat- 
ing and  cooking  devices  that  are  now  on  the  market.  Some  forms 
of  these  are  shown  in  Fig.  121. 

197.  Cost  of  Electric  Heating. — The  transformation  of  elec- 
trical energy  into  heat  by  means  of  a  resistance  takes  place  at  an 
efficiency  of  100  per  cent.  Nevertheless,  whether  it  is  cheaper  to 
heat  or  cook  with  electricity  than  with  some  other  transformation 
of  energy  into  heat  will  depend  upon  the  relative  cost  of  electrical 
and  other  forms  of  energy.  For  the  purpose  of  enabling  a  com- 
parison to  be  made,  Mr.  H.  O.  Swoboda,  in  the  Electric  Journal 
for  July,  1913,  published  the  following: 

COMPARATIVE   COST   OF   HEAT   GENERATED   BY   COAL   GAS 
AND  ELECTRICITY 

Coal  develops  at  an  average  a  heat  of  12,000  B.t.u.  per  pound.  The 
efficiency  of  coal-burning  heating  apparatus  averages  about  10  per  cent. 
Effective  heat  obtained  from  1  Ib.  of  coal  =1,200  B.t.u.;  from  1  short  ton 
of  coal  =2,400,000  B.t.u. 

Gas  develops  at  an  average  a  heat  of  660  B.t.u.  per  cubic  foot.  The 
efficiency  of  gas-burning  heating  apparatus  averages  about  20  per  cent. 
Effective  heat  obtained  from  1  cu.  ft.  of  gas  =132  B.t.u.;  from  1,000  cu.  ft. 
gas  =132,000  B.t.u. 

Electricity  develops  a  heat  of  3,413  B.t.u.  per  kw.-hr.  The  efficiency  of 
electrically  heated  apparatus  averages  about  80  per  cent.  Effective  heat 
obtained  from  1  kw.-hr.  =2,730  B.t.u. 

Based  on  these  figures,  the  same  amount  of  useful  or  effective  heat  is 
generated  by 

1  kw.-hr.  or  20  cu.  ft.  of  gas  or  2.25  Ib.  of  coal. 

A  table  of  comparison  showing  prices  at  which  electricity  would  have  to 
be  sold,  to  compete  with  coal  and  gas,  if  there  were  no  other  advantage  in 
using  electrically  generated  heat,  is  given  on  next  page. 

At  the  present  prices  for  electrical  energy  the  cost  of  heating  by 
electricity,  with  few  exceptions,  is  higher  than  by  coal  or  gas  and 
other  reasons  for  its  use  must  exist.  Although  many  reasons 
can  be  enumerated  why  electrical  energy  may  be  used  for  house- 
hold heating,  the  advantages  of  electrical  heating  may  be  summed 
up  under  one  heading,  convenience. 


WORK  AND  ENERGY 


205 


TABLE  IX 


Coal 
per  ton 

Electricity  per 
kilowatt-hour 

Gas  per 
1,000  cu.  ft. 

Electricity  per 
kilowatt-hour 

$1.50 

0.  17  cent 

$0.10 

0.2  cent 

2.00 

0.23  cent 

0.20 

0.4  cent 

2.50 

0.28  cent 

0.30 

0.6  cent 

3.00 

0.34  cent 

0.40 

0.8  cent 

3.50 

0.39  cent 

0.50 

1  .  0  cent 

4.00 

0.45  cent 

0.60 

1  .  2  cents 

4.50 

0.51  cent 

0.70 

.1.4  cents 

5.00 

0.57  cent 

0.80 

1.6  cents 

5.50 

0.62  cent 

0.90 

1  .  8  cents 

6.00 

0.68  cent 

1.00 

2  .  0  cents 

1.25 

2.5  cents 

1.50 

3  .  1  cents 

1.75 

3  .  6  cents 

RECAPITULATION 

1.  Work  is  defined  as  the  product  of  a  force  and  the  displacement 
produced  by  or  against  this  force  in  the  direction  of  the  force. 

(a)  The  unit  of  work  in  the  English  system  of  units  is  called  a  foot- 
pound.   The  foot-pound  is  the  work  done  in  lifting  a  weight  of  1 
Ib.  1  ft.  high  against  gravity. 

(b)  In  metric  units  the  unit  of  work  is  the  joule.     A  joule  is  equal  to 
10,000,000  ergs.     An  erg  is  the  work  done  by  a  force  of  one  dyne 
acting  through  a  distance  of  1  cm. 

2.  Energy  is  the  ability  of  doing  work.     The  units  for  measuring  energy 
are  the  same  as  those  for  work. 

3.  Power  is  the  time  rate  of  doing  work. 

(a)  The  English  unit  of  power  is  the  horse-power.     A  horse-power 
is  the  rate  of  doing  550  ft.-lb.  of  work  per  second. 

(b)  The  metric  unit  of  power  is  the  watt.    A  watt  is  the  rate  of 
doing  1  joule  per  second.     One  horse-power  =  746  watts. 

A  kilowatt  =  1,000  watts. 

4.  Work  in  direct-current  circuits  is  obtained  by  multiplying  volts  by 
amperes  by  time.    Algebraically  it  is  given  by 

Work  =  Elt 

The  commercial  unit  for  electrical  energy  or  work  is  the  kilowatt- 
hour.  A  kilowatt-hour  is  the  work  done  by  1  kw.  in  1  hour;  it  equals 
3,600,000  joules. 

5.  Power  in  direct-current  circuits  is  obtained  by  multiplying  volts 
by  amperes,  or 

Power  =  El  watts 


206  MAGNETISM  AND  ELECTRICITY 

6.  Power  drop  or  loss  is  the  loss  per  second  when  a  current  of  /  amperes 
flows  through  a  resistance  R.     It  is  equal  to  I*R  watts. 

7.  A  calorie  is  the  quantity  of  heat  required  to  raise  the  temperature  of 
1  grm.  of  water  from  15  to  16  degrees  cent.     One  calorie  =  4.181 
joules. 

A  British  thermal  unit  is  the  quantity  of  heat  required  to  change  the 
temperature  of  1  Ib.  of  water  1  degree  Fahrenheit.  One  B.t.u. 
=  252  calories. 

The  heat  generated  by  a  current  of  /  amperes  in  a  resistance  of  R 
ohms  in  time  t  seconds  is  given  by 

Heat  (calories)  =0.24  I*Rt.  calories 

=  0.24  watts Xt 
Heat  (B.t.u.)      =  0 . 00095  IzRt 

=  0.00095  watts X* 


INDEX 


Action  and  reaction  principle,  69 

Amalgamation,  90 

American  wire  gage,  129 

Ampere,  110 

Analogies  of  self-inductance,  84 

Analogy  for  capacity,  148 

for  electric  current,  110 

for  resistance,  123,  127,  128 
Anode,  107 
Arlington  wireless  sending  station, 

81 

Armature,  172,  174,  176 
Attraction,  3 

between  electric  wires,  28 

between  like  poles,  10 

between  unlike  poles,  9 

law  of,  3 

variation  of,  with  distance,  4 


Bar  magnets,  3 

Battery,  resistance  of  cells,  165 

in  parallel,  166 

in  series,  165 

Best  grouping  of  cells,  168 
Bismuth,  effect  of  magnetic  field  on, 

14 

British  thermal  unit,  201 
Brushes,  175 
Buckling  of  storage  cell  plates,  113 


Calculation  of  joint  resistance,  157, 

159 

of  resistance,  134 
Calorie,  201 
Capacity,  148 

Carbon  filament  lamps,  202 
Cathode,  107 


Cause  of  rotation  of  motor  armature, 

181 

Cells,  best  grouping  of,  168 
kinds  of,  97 
in  parallel,  165 
in  series,  163 
in  series-parallel,  166 
primary,  97 
storage,  97,  110 

Change  of  resistance  with  tempera- 
ture, 136 

Characteristics  of  a  separately  ex- 
cited motor,  184 
Chemical  action  in  a  simple  cell,  90 

in  a  storage  cell,  112 
Circular  coil,  magnetic  field  of,  31 
Circular  mil,  129 
Coefficient,  temperature  resistance, 

140 

Coercive  force,  44 
Commutator,  172,  175 
Compound  generator,  179 
motor,  190 

cumulative,  190 
differential,  190 
Condenser,  148,  149 
Conductors,  91 
Conservation  of  energy,  195 
Contacts,  resistance  of,  141 
Coordinates,  signs  of,  38 
.Copper  wire  table,  131 
Cost  of  electric  heating,  204 
Coulomb,  110 

Counter  e.m.f.  of  polarization,  96 
Current  electricity,  89 
flow  in  a  circuit,  143 
relation  between  primary  and 

induced  e.m.f.,  75 
decay  of,  in  inductive  circuit,  83 
primary,  76 

rise  of,  in  inductive  circuit,  83 
secondary   76 
unit  of,  32 


207 


208 


INDEX 


Curve  plotting,  38 

Curves  for  voltage  of  a  lead  storage 

cell,  114 
of  nickel  iron  storage  cell,  118 


D 


Daniell  cell,  99 

Decay  of  current  in  an  inductive 
circuit,  83 

Declination,  17 

Development  of  an  e.m.f.  by  electro- 
magnets, 72 
of  magnetism  in  an  iron  core,  33 

Dip,  17 

Direction  of  magnetic  field  around 
an  electric  wire,  rule  for,  26 

Dissociation  theory,  107 

Drop,  voltage,  151 

Dry  cell,  98 

Dyne,  5 


E 


Earth's  magnetism,  15 
Edison  primary  cell,  98 
Effect  of  electric  current  on  mag- 
netic needle,  24 
of  heat  on  magnetisn,  14 
of  self-inductance,  85 
Electrical  capacity,  148 

current  flow  in  a  circuit,  143 

heating  value,  200 
resistance,  123 
work,  197 

Electric  current,  unit  of,  32 
generator,  171 
kinds  of,  178 
lamps,  202 

carbon  filament,  202 
flaming  arc,  203 
tungsten,  202 
motor,  181 
wire,  23 

wires,  reaction  between,  28 
Electricity  and  electrical  energy,  197 

current,  89 

Electro-chemical  equivalent,  110 
Electrodes,  91 


Electrodynamometer   ammeter,    29, 

30 
Electrolysis,  105 

Faraday's  laws,  108 
Electrolytic  processes,  120 
Electromagnetic  induction,  65 

law  of,  70 

theory  of,  68 
Electromagnetism,  23 
Electromagnets,  33 

lifting  force  of,  57 

of  a  generator,  63 
Electromotive  force,  176 

dependence  upon  speed,  176 
upon    strength    of    magnetic 

field,  177 

Electromotive  force  or  pressure,  93 
Electroplating,  118 
Energy,  193 

kinetic,  195 

potential,  195 

Energy,  expenditure  of  in  an  elec- 
tric circuit,  96 

Energy  in  a  magnetic  field,  84 
Erg,  193 

Examples  of  self-inductance,  86 
Expenditure  of  energy  in  an  electric 
circuit,  96,  109 


Faraday's  laws,  108 

Field  rheostat,  161 

Flaming  arc  lamp,  203 

Flow  of  current  in  a  circuit,  143 

Flux  density,  36,  44,  45,  59 

Foot-pound,  193 

Force,  5 

between  magnet  poles,  5 
between    two    current    bearing 

wires,  28 

tending  to  draw  two  poles  to- 
gether, 59 

Frictional  resistance,  43 


Gage  numbers,  130 
Galvanoscope,  66 


INDEX 


209 


Generator  electromagnets,  63 
Gravity  cell,  100 


II 


Heat,  effect  of,  on  magnetism,  14 
Heating  value  of  electric  current,  200 
Henry,  Joseph,  35 

investigations    in     electromag- 

netism,  35 
Heusler's  alloy,  2 
Horse- power,  196 
Hysteresis,  magnetic,  42 

loop,  43 

loss,  44,  46 


Induced  electromotive  force,  71,  176 
dependence  upon  speed,  176 
dependence    upon    strength    of 

magnetic  field,  177 
unit  of,  71 
Induction  coil,  78 

electromagnetic,  65 
of  e.m.f.  by  electromagnets,  73 
magnetic,  13 

Installation  of  storage  battery,  115 
Insulators,  105 


Joint  resistance,  rule  for,  157,  160 
Joule,  193 

K 

Key,  telegraph,  49 
Kinds  of  cells,  97 

one-fluid,  97 

primary,  97 

secondary,  97 

two-fluid,  99 
Kinds  of  generators,  178 

compound,  179 

magneto,  178 

series,  179 

shunt,  179 

Kinetic  theory  of  matter,  15 
22 


Law  of  electromagnetic  induction,  70 
Laws  of  magnetic  attraction,  3 

between  magnet  poles,  9 
Lead  storage  cell,  112 
Le  Clanche  cell,  97 
Lifting  force  of  electromagnets,  57 
Lifting  magnets,  55 
Liquid  conductors,  91,  105 

electrolytes,  105 

insulators,  105 
Local  action,  91 
Lodestone,  properties  of,  2 
Loop-hysteresis,  43 


M 


Magnetic  attraction,  laws  of,  3 
Magnetic  field,  6 

around  two  bar  magnets,  9 

inside  of  a  long  solenoid,  36 

of  a  circular  coil,  31 

of  commercial  motors,  186 

of  the  earth,  15,  16 

of  two  unlike  bar  magnets,  9 

produced  by  a  current,  24 

representation  of,  6,  7,  8 

unit  field,  7 

Magnetic  hysteresis,  42 
Magnetic  induction,  13 
Magnetic  properties  of  a  U-shaped 

bar,  34 

Magnetic  properties  of  solenoids,  25 
Magnetic  substances,  2,  14 
Magnetism,  1 

definition  of,  1 

derivation  of  word,  2 

effect  of  heat  on,  14 

molecular,  10 

of  the  earth,  15 
Magnetism,  residual,  44 
Magnetization  curve,  37 
Magneto  generator,  178 
Magnetomotive  force,  41 
Magnets,  2 

forms  of,  3 

lifting,  55 

methods  of  making,  2 


210 


INDEX 


Magnets,  permanent,  2 
poles  of,  3 
properties  of,  2 
properties  of  space  around  bar 

magnets,  6 
temporary,  2 

Material,  influence  of  on  the  resist- 
ance of  a  conductor,  133 
Measurement  of  wire,  129 
Mil,  129 
Molecular  theory  of  magnetism,  10, 

12 

Motor  rheostats,  162,  163 
Motors,  electric,  181 
compound,  190 

relation  between  the  strength  of 
the     magnetic     field     and 
speed  of  rotation,  183 
rotation  of  armature,  cause  of, 

181 
shunt,  190 

N 

Newton's  third  law,  69 
Nickel-iron  storage  cells,  114 


Ohm,  134 

Ohm's  law,  143,  145 

verification  of,  144 
One  fluid  cells,  97 
Ozonator,  120 


Parallel  connection,  160 

of  cells,  165 

of  lamps,  160 
Parallel  connection    of    resistances, 

154,  156 

Paramagnetic  substances,  14 
Permeability,  36 
Plotting  a  point,  39 
Polarity  of  a  solenoid,  27 
Polarization,  96 
Poles  of  a  magnet,  3 

attraction  and  repulsion  of,  9 

unit  pole,  5 
Power,  196 

drop,  199 


Power,  units  of,  196 

Practical  application  of  permanent 

magnets,  18 
electric  meters,  19 
magneto  ringer,  18 
mariner's  compass,  18 
surveyor's  compass,  17 
telephone  receiver,  18 
watthour  meter,  20 
Practical    applications    of    electro- 
magnetism,  47 
electric  bell,  47 
electromagnetic  induction,  77 
lifting  magnets,  55 
self-induction,  87 
telegraph,  48 
telephone,  51 
Practical    applications    of    primary 

cells,  102 
Practical  applications  of  resistances, 

160 

Practical  applications  of  the  heating 
effect  of  electric  currents, 
202 

Practical  effects  of  resistance  varia- 
tions with  temperature,  138 
Primary  and  secondary  coils,  76 
Primary  current  and  induced  e.m.f., 

75 

Principle    of    inducing    an    electro- 
motive force,  70 
Principle    of    the    conservation    of 

energy,  195 
Principles  of  the  electric  generator, 

171 
Principles    of    electrodynamometer 

ammeter,  29,  30 
Properties  of  solenoids,  25 
Properties  of  space   surrounding  a 
magnet,  6 


Q 

Quadrants,  38 

Quantity  of  electricity,  110,  197 

R 

Recapitulation    of    electromagnetic 
principles,  44 


INDEX 


211 


Recapitulation,    of    generator    and 
motor  principles,  190 
of  magnetic  principles,  20 
of  principles  of  current  flow,  169 
of  principles  of  electrolysis,  120 
of  principles  of  electromagnetic 

induction,  88 
of  principles  of  primary  cells, 

103 

of  principles  of  resistance,  141 
of  some  applications  of  electro- 
magnets, 63 
of  work  and  energy  principles, 

205 

Reaction  between  electric  wires,  28 
Receiving  apparatus,  wireless,  81 
Relation  between  primary  current 

and  induced  e.m.f.,  75 
Relay,  telegraph,  50 
Residual  magnetism,  44 
Resistance,  123  • 
board,  124 
calculation  of,  134 
dependence  upon  the  material 

of  the  conductor,  133 
specific,  134 

temperature  effect  on,  136 
thermometer,  139 
unit  of,  134 
of  cells,  165 
in  parallel,  166 
in  series,  165 
of  contacts,  141 
temperature  coefficient,  140    . 
alloys,  140 
manganin,  140 
metals,  140 
Resistances,  149 
in  parallel,  154 
in  series,  149 
Resistivity,  135 

table  of,  136 
Rheostats,  161,  162 
Rise  of  a  current  in  an  inductive 

circuit,  83 

of  voltage  in  a  simple  cell,  94 
Rotation  of  motor  armature,  181 
cause  of,  181 
direction  of,  183 


Rotation,  relation  between  strength 

of  magnetic  field  and  speed, 

183 
Rule  for  determining  the  polarity  of 

a  solenoid,  27 
for  the   direction   of   magnetic 

field    around    an    electric 

wire,  26 


S 


Secondary  cells,  110 
Self-inductance,  analogy  for,  84 

calculation  of,  85 

definition,  85 

effect  of,  85 

examples  of,  86 

Sending  apparatus,  wireless,  80 
Separately  excited  motor,  184 
Series,  connection  of  cells,  163 

connection  of  resistances,  149 

-parallel  connection  of  cells,  166 

generator,  operation,  179,  188 
Shunt  generator,  operation  of,  179 

motor,  190 

Signs  of  coordinates,  38 
Solenoids,  25 
Solid  conductors,  91 
Sounder,  telegraph,  49 
Specific  resistance,  134,  135 
Storage  cells,  110 

lead,  112 

nickel-iron,  114 

Strength  at  center  of  a  circular  coil, 
31 

of  electromagnets,  34 

of    magnetic    field    around    an 

electric  wire,  27 

Summary  of  principles  of  the  mag- 
netic circuit,  60 


Table  for  standard  annealed  copper 
wire,  131 

of  restivity  of  metallic  wires,  136 
Telegraph,  48 

key  sounder,  49 

relay,  50 


212 


INDEX 


Telephone  circuit,  79 

receiver,  51,  54 

switchboard,  52 

terminal  room,  53 

Temperature,  influence  of,  on  resist- 
ance,. 136 

Thermometer,  resistance,  139 
Three  or  more  conductors  in  parallel, 

159 

Traction  and  magnetizing  force,  60 
Tungsten  lamps,  202 


U 


Unit  magnetic  field,  7 

magnet  pole,  definition,  5 

of  current,  32 

of  induced  electromotive  force, 

71 

of  resistance,  134 
of  work,  193 


Volt,  72,  95 

Voltage  drop,  151 

Voltaic  cell,  91 

Volt  ammeter,  91 

Voltage  of  a  dry  cell,  98 

of  a  lead  storage  cell,  114 
of  a  Leclanche  cell,  98 
of  an  Edison  cell,  98 
of  a  nickel-iron  cell,  118 
of  a  simple  cell,  94 

W 

Wireless  sending  apparatus,  81 
Wireless  telegraph,  circuit,  80 
Wire  measurement,  129 
Wire  table,  131 
Work  and  energy,  193 

unit  of,  193 

watt,  196 


LOAN  OEPT 


